Scaling Law for Irreversible Entropy Production in Critical Systems.
Hoang, Danh-Tai; Prasanna Venkatesh, B; Han, Seungju; Jo, Junghyo; Watanabe, Gentaro; Choi, Mahn-Soo
2016-06-09
We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise in a single setup with equal significance. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. The initially ordered spins become disordered by quenching the ferromagnetic coupling constant. For a sudden quench, the deviation from the Jarzynski equality evaluated from the ideal ensemble average could, in principle, depend on the reduced coupling constant ε0 of the initial state and the system size L. We find that, instead of depending on ε0 and L separately, this deviation exhibits a scaling behavior through a universal combination of ε0 and L for a given tolerance parameter, inherited from the critical scaling laws of second-order phase transitions. A similar scaling law can be obtained for the finite-speed quench as well within the Kibble-Zurek mechanism.
International Nuclear Information System (INIS)
Rau, J.
1993-01-01
In the presence of strong gravitational, electromagnetic or other gauge fields, particle-antiparticle pairs are created out of the vacuum. Creation processes of this type are responsible for, e.g., hadron production in heavy ion collisions or the radiation of black holes. They lead to an increase in entropy, thus contributing to the thermalization of the system under consideration. This suggests that particle creation in strong fields is an irreversible process. Key issues to be addressed are: (1) under which conditions particle creation is indeed irreversible, and how this can be reconciled with the time-reversal invariance of the underlying microscopic dynamics: (ii) if-and if so, how-particle creation can be described within the framework of a theory of nonequilibrium processes: (iii) how the associated entropy is defined; and (iv) how particle creation can be incorporated into a kinetic equation that also accounts for subsequent acceleration and collisions. These issues are studied by means of the projection method. After a comprehensive introduction to that method, it is applied to a simple model from quantum electrodynamics which incorporates acceleration, collisions, and pair creation due to the Schwinger mechanism. For this model, the author obtains: (1) the complete set of time scales, which furnishes a precise mathematical criterion for the irreversibility of particle creation; (2) the associated relevant entropy to which the H-theorem applies; and (3) a generalization of the quantum Boltzmann equation which includes a source term derived from first principles
Entropy, Extropy and the Physical Driver of Irreversibility
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Attila Grandpierre
2012-06-01
Full Text Available We point out that the fundamental irreversibility of Nature requires the introduction of a suitable measure for the distance from equilibrium. We show that entropy, which is widely held to be such a measure, suffers from the problem that it does not have a physical meaning, since it is introduced on the basis of mathematical arguments. As a consequence, the basic physics beyond irreversibility has remained obscure. We present here a simple but transparent physical approach for solving the problem of irreversibility. This approach shows that extropy, the fundamental thermodynamic variable introduced by Katalin Martinás, is the suitable measure for the distance from equilibrium, since it corresponds to the actual driver of irreversible processes. Since extropy explicitly contains in its definition all the general thermodynamic forces that drive irreversible processes, extropy is the suitable physical measure of irreversibility.
Equipartition of entropy production
International Nuclear Information System (INIS)
Tondeur, D.
1990-01-01
This paper deals with the optimal design or operation of heat and mass transfer processes and develops the following conjecture: for a given duty, the best configuration of the process is that in which the entropy production rate is most uniformly distributed. This principle is first analyzed in detail on the simple example of tubular heat exchangers, and within the framework of linear irreversible thermodynamics. A main result is established, which states that the total entropy production is minimal when the local production is uniformly distributed (equipartition). Corollaries then result, which relate the entropy production and the variance of its distribution to economic factors such as the duty, the exchange area, the fluid flow-rates, and the temperature changes. The equipartition principle is then extended to multiple independent variables (time and space), multicomponent transfer, and non-linear but concave flux vs force relationship. Chemical Engineering examples are discussed, where the equipartition property has been applied implicitly or explicitly: design of distillation plates, cyclic distillation, optimal state of feed, and flow-sheets in chromatographic separations. Finally, a generalization of the equipartition principle is proposed, for systems with a distributed design variable (such as the size of the various elements of a system). The optimal distribution of investment is such that the investment in each element (properly amortized) is equal to the cost of irreversible energy degradation in this element. This is equivalent to saying that the ratio of these two quantities is uniformly distributed over the system, and reduces to equipartition of entropy production when the cost factors are constant over the whole system
Irreversible entropy model for damage diagnosis in resistors
Energy Technology Data Exchange (ETDEWEB)
Cuadras, Angel, E-mail: angel.cuadras@upc.edu; Crisóstomo, Javier; Ovejas, Victoria J.; Quilez, Marcos [Instrumentation, Sensor and Interfaces Group, Electronic Engineering Department, Escola d' Enginyeria de Telecomunicació i Aeronàutica de Castelldefels EETAC, Universitat Politècnica de Catalunya, Barcelona Tech (UPC), Castelldefels-Barcelona (Spain)
2015-10-28
We propose a method to characterize electrical resistor damage based on entropy measurements. Irreversible entropy and the rate at which it is generated are more convenient parameters than resistance for describing damage because they are essentially positive in virtue of the second law of thermodynamics, whereas resistance may increase or decrease depending on the degradation mechanism. Commercial resistors were tested in order to characterize the damage induced by power surges. Resistors were biased with constant and pulsed voltage signals, leading to power dissipation in the range of 4–8 W, which is well above the 0.25 W nominal power to initiate failure. Entropy was inferred from the added power and temperature evolution. A model is proposed to understand the relationship among resistance, entropy, and damage. The power surge dissipates into heat (Joule effect) and damages the resistor. The results show a correlation between entropy generation rate and resistor failure. We conclude that damage can be conveniently assessed from irreversible entropy generation. Our results for resistors can be easily extrapolated to other systems or machines that can be modeled based on their resistance.
Irreversible entropy model for damage diagnosis in resistors
International Nuclear Information System (INIS)
Cuadras, Angel; Crisóstomo, Javier; Ovejas, Victoria J.; Quilez, Marcos
2015-01-01
We propose a method to characterize electrical resistor damage based on entropy measurements. Irreversible entropy and the rate at which it is generated are more convenient parameters than resistance for describing damage because they are essentially positive in virtue of the second law of thermodynamics, whereas resistance may increase or decrease depending on the degradation mechanism. Commercial resistors were tested in order to characterize the damage induced by power surges. Resistors were biased with constant and pulsed voltage signals, leading to power dissipation in the range of 4–8 W, which is well above the 0.25 W nominal power to initiate failure. Entropy was inferred from the added power and temperature evolution. A model is proposed to understand the relationship among resistance, entropy, and damage. The power surge dissipates into heat (Joule effect) and damages the resistor. The results show a correlation between entropy generation rate and resistor failure. We conclude that damage can be conveniently assessed from irreversible entropy generation. Our results for resistors can be easily extrapolated to other systems or machines that can be modeled based on their resistance
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Beretta, Gian Paolo
2008-02-01
Full Text Available What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? Most physicists still accept and teach that the rationalization of these fundamental questions is given by Statistical Mechanics. Indeed, for everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions allows a successful description of the thermodynamic equilibrium properties of matter, including entropy values. However, as already recognized by Schrodinger in 1936, Statistical Mechanics is impaired by conceptual ambiguities and logical inconsistencies, both in its explanation of the meaning of entropy and in its implications on the concept of state of a system. An alternative theory has been developed by Gyftopoulos, Hatsopoulos and the present author to eliminate these stumbling conceptual blocks while maintaining the mathematical formalism so successful in applications. To resolve both the problem of the meaning of entropy and that of the origin of irreversibility we have built entropy and irreversibility into the laws of microscopic physics. The result is a theory, that we call Quantum Thermodynamics, that has all the necessary features to combine Mechanics and Thermodynamics uniting all the successful results of both theories, eliminating the logical inconsistencies of Statistical Mechanics and the paradoxes on irreversibility, and providing an entirely new perspective on the microscopic origin of irreversibility, nonlinearity (therefore including chaotic behavior and maximal-entropy-generation nonequilibrium dynamics. In this paper we discuss the background and formalism of Quantum Thermodynamics including its nonlinear equation of motion and the main general results. Our objective is to show in a not-too-technical manner that this theory provides indeed a
International Nuclear Information System (INIS)
Luo Qiang; Schwarz, Bjoern; Mattern, Norbert; Eckert, Juergen
2010-01-01
We study the effects of amorphous structure and random anisotropy on the magnetic entropy change in a series of Tb-based amorphous alloys. The amorphous structure broadens the peak of magnetic entropy change and facilitates the adjustment of properties. The peak magnetic entropy change above the spin freezing temperature first depends on the average magnetic moment approximately linearly and second on the exchange interaction and random anisotropy. Large and broad reversible negative magnetic entropy changes are observed above the spin freezing temperature and giant positive irreversible magnetic entropy changes which associate with the internal entropy production are obtained well below.
Entropy equilibrium equation and dynamic entropy production in environment liquid
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.
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Leonid M. Martyushev
2015-06-01
Full Text Available The entropy production (inside the volume bounded by a photosphere of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.
Minimum entropy production principle
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel
2013-01-01
Roč. 8, č. 7 (2013), s. 9664-9677 ISSN 1941-6016 Institutional support: RVO:68378271 Keywords : MINEP Subject RIV: BE - Theoretical Physics http://www.scholarpedia.org/article/Minimum_entropy_production_principle
Entropy Production in Stochastics
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Demetris Koutsoyiannis
2017-10-01
Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.
Irreversible thermodynamics of dark energy on the entropy-corrected apparent horizon
Energy Technology Data Exchange (ETDEWEB)
Karami, K; Sahraei, N [Department of Physics, University of Kurdistan, Pasdaran Street, Sanandaj (Iran, Islamic Republic of); Jamil, M, E-mail: KKarami@uok.ac.i, E-mail: mjamil@camp.nust.edu.p [Center for Advanced Mathematics and Physics (CAMP), National University of Sciences and Technology (NUST), Islamabad (Pakistan)
2010-10-15
We study the irreversible (non-equilibrium) thermodynamics of the Friedmann-Robertson-Walker (FRW) universe containing only dark energy. Using the modified entropy-area relation that is motivated by loop quantum gravity, we calculate the entropy-corrected form of the apparent horizon of the FRW universe.
Gradient Dynamics and Entropy Production Maximization
Janečka, Adam; Pavelka, Michal
2018-01-01
We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell-Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
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Rodrigo Cofré
2018-01-01
Full Text Available The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.
A Derivation of a Microscopic Entropy and Time Irreversibility From the Discreteness of Time
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Roland Riek
2014-06-01
Full Text Available The basic microsopic physical laws are time reversible. In contrast, the second law of thermodynamics, which is a macroscopic physical representation of the world, is able to describe irreversible processes in an isolated system through the change of entropy ΔS > 0. It is the attempt of the present manuscript to bridge the microscopic physical world with its macrosocpic one with an alternative approach than the statistical mechanics theory of Gibbs and Boltzmann. It is proposed that time is discrete with constant step size. Its consequence is the presence of time irreversibility at the microscopic level if the present force is of complex nature (F(r ≠ const. In order to compare this discrete time irreversible mechamics (for simplicity a “classical”, single particle in a one dimensional space is selected with its classical Newton analog, time reversibility is reintroduced by scaling the time steps for any given time step n by the variable sn leading to the Nosé-Hoover Lagrangian. The corresponding Nos´e-Hoover Hamiltonian comprises a term Ndf kB T ln sn (kB the Boltzmann constant, T the temperature, and Ndf the number of degrees of freedom which is defined as the microscopic entropy Sn at time point n multiplied by T. Upon ensemble averaging this microscopic entropy Sn in equilibrium for a system which does not have fast changing forces approximates its macroscopic counterpart known from thermodynamics. The presented derivation with the resulting analogy between the ensemble averaged microscopic entropy and its thermodynamic analog suggests that the original description of the entropy by Boltzmann and Gibbs is just an ensemble averaging of the time scaling variable sn which is in equilibrium close to 1, but that the entropy
Maximum entropy production rate in quantum thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Beretta, Gian Paolo, E-mail: beretta@ing.unibs.i [Universita di Brescia, via Branze 38, 25123 Brescia (Italy)
2010-06-01
In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible
Multiscale analysis of heart rate dynamics: entropy and time irreversibility measures.
Costa, Madalena D; Peng, Chung-Kang; Goldberger, Ary L
2008-06-01
Cardiovascular signals are largely analyzed using traditional time and frequency domain measures. However, such measures fail to account for important properties related to multiscale organization and non-equilibrium dynamics. The complementary role of conventional signal analysis methods and emerging multiscale techniques, is, therefore, an important frontier area of investigation. The key finding of this presentation is that two recently developed multiscale computational tools--multiscale entropy and multiscale time irreversibility--are able to extract information from cardiac interbeat interval time series not contained in traditional methods based on mean, variance or Fourier spectrum (two-point correlation) techniques. These new methods, with careful attention to their limitations, may be useful in diagnostics, risk stratification and detection of toxicity of cardiac drugs.
Directory of Open Access Journals (Sweden)
Hou Hucan
2017-01-01
Full Text Available Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.
Entropy production for closed, open and third-kind systems
Energy Technology Data Exchange (ETDEWEB)
Sertorio, L.; Tinetti, G. [Turin Univ. (Italy). Dipt. di Fisica Teorica
1999-07-01
The authors refer to nonequilibrium thermodynamics where the concept of entropy production in defined. Remember that the formalism of equilibrium thermodynamics describes reversible transformations; in this formalism entropy is a state function, for a infinitesimal transformation they have dS=dQ{sub r}ev/T, entropy grows if heat is received, diminishes if heat is released and remains unchanged if the transformation is adiabatic, dQ=O. The formulation of nonequilibrium thermodynamic is not unique, they are two version, one discrete and one continuous: 1) Onsager formulation (1): ordinary differential equations. 2) Landau formulation (2): irreversible field theory. The two formulations do not differ in physical content, in fact the discrete formalism can be considered as a reduction of the continuous formalism and conversely the discrete formalism can be generalised to the continuous one, The continuous, or field theoretical approach, has the advantage that it leads to a spontaneous extension to the relativistic formalism (2). Regardless of the choice 1. or 2., in nonequilibrium thermodynamics any irreversibility is taken into account explicitly, the irreversible event begin: heat diffusion, viscosity and chemical reactions. The distinction among close and open systems applies to equilibrium and nonequilibrium thermodynamics as well.
Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro
2017-08-01
In this second part, we analyze the dissipation properties of generalized Poisson-Kac (GPK) processes, considering the decay of suitable L 2-norms and the definition of entropy functions. In both cases, consistent energy dissipation and entropy functions depend on the whole system of primitive statistical variables, the partial probability density functions \\{ p_α({x}, t) \\}α=1N , while the corresponding energy dissipation and entropy functions based on the overall probability density p({x}, t) do not satisfy monotonicity requirements as a function of time. These results provide new insights on the theory of Markov operators associated with irreversible stochastic dynamics. Examples from chaotic advection (standard map coupled to stochastic GPK processes) illustrate this phenomenon. Some complementary physical issues are also addressed: the ergodicity breaking in the presence of attractive potentials, and the use of GPK perturbations to mollify stochastic field equations.
Entropy and Entropy Production: Old Misconceptions and New Breakthroughs
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Leonid M. Martyushev
2013-03-01
Full Text Available Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings. The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it.
Memory behaviors of entropy production rates in heat conduction
Li, Shu-Nan; Cao, Bing-Yang
2018-02-01
Based on the relaxation time approximation and first-order expansion, memory behaviors in heat conduction are found between the macroscopic and Boltzmann-Gibbs-Shannon (BGS) entropy production rates with exponentially decaying memory kernels. In the frameworks of classical irreversible thermodynamics (CIT) and BGS statistical mechanics, the memory dependency on the integrated history is unidirectional, while for the extended irreversible thermodynamics (EIT) and BGS entropy production rates, the memory dependences are bidirectional and coexist with the linear terms. When macroscopic and microscopic relaxation times satisfy a specific relationship, the entropic memory dependences will be eliminated. There also exist initial effects in entropic memory behaviors, which decay exponentially. The second-order term are also discussed, which can be understood as the global non-equilibrium degree. The effects of the second-order term are consisted of three parts: memory dependency, initial value and linear term. The corresponding memory kernels are still exponential and the initial effects of the global non-equilibrium degree also decay exponentially.
Ecological optimization for generalized irreversible Carnot refrigerators
International Nuclear Information System (INIS)
Chen Lingen; Zhu Xiaoqin; Sun Fengrui; Wu Chih
2005-01-01
The optimal ecological performance of a Newton's law generalized irreversible Carnot refrigerator with the losses of heat resistance, heat leakage and internal irreversibility is derived by taking an ecological optimization criterion as the objective, which consists of maximizing a function representing the best compromise between the exergy output rate and exergy loss rate (entropy production rate) of the refrigerator. Numerical examples are given to show the effects of heat leakage and internal irreversibility on the optimal performance of generalized irreversible refrigerators
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
Cofré, Rodrigo; Maldonado, Cesar
2018-01-01
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.
IRREVERSIBILITY GENERATION IN SUGAR, ALCOHOL AND BIOGAS INTEGRATED PRODUCTIONS
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Meilyn González Cortés
2017-01-01
Full Text Available In this work, the stages of losses and lower exergetic efficiency are determined when the sugar production process is integrated with others for the production of products such as biogas, torula yeast and electricity. The study is carried out in three scenarios of integrated processes for obtaining the indicated products. A sugar factory in which sugar and electricity are produced is considered as the base scenario and from this; a second scenario is inferred in which alcohol is produced from the molasses of the sugar process and biogas from the vinasse of the alcohol distillation process. Finally, a third scenario is exergetically evaluated in which sugar, electricity, biogas and alcohol are produced, but this last one from juices and molasses of the sugar process. For the exergetic analysis the integrated scheme was divided into 8 subsystems. From the analysis of results, the major subsystems that generate irreversibilities are: cogeneration (64.36-65.98%, juice extraction (8.85-9.85%, crystallization and cooking, (8.48 -9.02%, fermentation (4.12-4.94% and distillation (2.74-3.2%. Improvements are proposed to minimize irreversibilities, including the thermal integration of processes, technological modifications in the fermentation process and the introduction of more efficient equipment for the generation of electricity. The exergetic efficiency is between 78.95-81.10%, obtaining greater exergetic efficiency in the scheme of joint operation to produce sugar, alcohol and biogas.
Optimal paths of piston motion of irreversible diesel cycle for minimum entropy generation
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Ge Yanlin
2011-01-01
Full Text Available A Diesel cycle heat engine with internal and external irreversibility’s of heat transfer and friction, in which the finite rate of combustion is considered and the heat transfer between the working fluid and the environment obeys Newton’s heat transfer law [q≈ Δ(T], is studied in this paper. Optimal piston motion trajectories for minimizing entropy generation per cycle are derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston motion trajectories for the cases of with piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments, respectively. Numerical examples for optimal configurations are provided, and the results obtained are compared with those obtained when maximizing the work output with Newton’s heat transfer law. The results also show that optimizing the piston motion trajectories could reduce engine entropy generation by more than 20%. This is primarily due to the decrease in entropy generation caused by heat transfer loss on the initial portion of the power stroke.
The Gibbs entropy production in general relativity
International Nuclear Information System (INIS)
Henneaux, M.
1983-01-01
The entropy production is analyzed in the case of homogeneous cosmological models of the Bianchi type. It is shown to vanish for class-A models and to be undefined for class-B ones, because of an ambiguity in the measure on the space of the true gravitational degrees of freedom. How this results extend to the full Einstein theory is discussed
Gibbs entropy production in general relativity
International Nuclear Information System (INIS)
Henneaux, M.
1983-01-01
The entropy production is analyzed in the case of homogeneous cosmological models of the Bianchi type. It is shown to vanish for class-A models and to be undefined for class-B ones, because of an ambiguity in the measure on the space of the true gravitational degrees of freedom. How this results extends to the full Einstein theory is discussed
Extremum principles for irreversible processes
International Nuclear Information System (INIS)
Hillert, M.; Agren, J.
2006-01-01
Hamilton's extremum principle is a powerful mathematical tool in classical mechanics. Onsager's extremum principle may play a similar role in irreversible thermodynamics and may also become a valuable tool. His principle may formally be regarded as a principle of maximum rate of entropy production but does not have a clear physical interpretation. Prigogine's principle of minimum rate of entropy production has a physical interpretation when it applies, but is not strictly valid except for a very special case
Entropy production in a box: Analysis of instabilities in confined hydrothermal systems
Börsing, N.; Wellmann, J. F.; Niederau, J.; Regenauer-Lieb, K.
2017-09-01
We evaluate if the concept of thermal entropy production can be used as a measure to characterize hydrothermal convection in a confined porous medium as a valuable, thermodynamically motivated addition to the standard Rayleigh number analysis. Entropy production has been used widely in the field of mechanical and chemical engineering as a way to characterize the thermodynamic state and irreversibility of an investigated system. Pioneering studies have since adapted these concepts to natural systems, and we apply this measure here to investigate the specific case of hydrothermal convection in a "box-shaped" confined porous medium, as a simplified analog for, e.g., hydrothermal convection in deep geothermal aquifers. We perform various detailed numerical experiments to assess the response of the convective system to changing boundary conditions or domain aspect ratios, and then determine the resulting entropy production for each experiment. In systems close to the critical Rayleigh number, we derive results that are in accordance to the analytically derived predictions. At higher Rayleigh numbers, however, we observe multiple possible convection modes, and the analysis of the integrated entropy production reveals distinct curves of entropy production that provide an insight into the hydrothermal behavior in the system, both for cases of homogeneous materials, as well as for heterogeneous spatial material distributions. We conclude that the average thermal entropy production characterizes the internal behavior of hydrothermal systems with a meaningful thermodynamic measure, and we expect that it can be useful for the investigation of convection systems in many similar hydrogeological and geophysical settings.
International Nuclear Information System (INIS)
Dobbertin, R.
1976-01-01
Functional relations are derived which link the reduced distribution functions of a classical N-particle system through the entropy production due to microscopic deviations from hamiltonian dynamics. These relations have been used in an earlier paper for the closure of the BBGKY-hierarchy and may be useful for the establishment of collective particle models in particular and the understanding of irreversibility in general. (Auth.)
The maximum entropy production and maximum Shannon information entropy in enzyme kinetics
Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš
2018-04-01
We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.
Entropy production in a cell and reversal of entropy flow as an anticancer therapy
Institute of Scientific and Technical Information of China (English)
Liao-fu LUO
2009-01-01
The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and low- intensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently re- verse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the bio- logical tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful infor- marion from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.
Excess Entropy Production in Quantum System: Quantum Master Equation Approach
Nakajima, Satoshi; Tokura, Yasuhiro
2017-12-01
For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by ln \\breve{ρ }_0 and ρ _0 where ρ _0 is the instantaneous steady state of the QME and \\breve{ρ }_0 is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.
Montefusco, Alberto; Consonni, Francesco; Beretta, Gian Paolo
2015-04-01
By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves.
Kleidon, Axel
2009-06-01
The Earth system is maintained in a unique state far from thermodynamic equilibrium, as, for instance, reflected in the high concentration of reactive oxygen in the atmosphere. The myriad of processes that transform energy, that result in the motion of mass in the atmosphere, in oceans, and on land, processes that drive the global water, carbon, and other biogeochemical cycles, all have in common that they are irreversible in their nature. Entropy production is a general consequence of these processes and measures their degree of irreversibility. The proposed principle of maximum entropy production (MEP) states that systems are driven to steady states in which they produce entropy at the maximum possible rate given the prevailing constraints. In this review, the basics of nonequilibrium thermodynamics are described, as well as how these apply to Earth system processes. Applications of the MEP principle are discussed, ranging from the strength of the atmospheric circulation, the hydrological cycle, and biogeochemical cycles to the role that life plays in these processes. Nonequilibrium thermodynamics and the MEP principle have potentially wide-ranging implications for our understanding of Earth system functioning, how it has evolved in the past, and why it is habitable. Entropy production allows us to quantify an objective direction of Earth system change (closer to vs further away from thermodynamic equilibrium, or, equivalently, towards a state of MEP). When a maximum in entropy production is reached, MEP implies that the Earth system reacts to perturbations primarily with negative feedbacks. In conclusion, this nonequilibrium thermodynamic view of the Earth system shows great promise to establish a holistic description of the Earth as one system. This perspective is likely to allow us to better understand and predict its function as one entity, how it has evolved in the past, and how it is modified by human activities in the future.
Frenetic Bounds on the Entropy Production
Maes, Christian
2017-10-01
We give a systematic derivation of positive lower bounds for the expected entropy production (EP) rate in classical statistical mechanical systems obeying a dynamical large deviation principle. The logic is the same for the return to thermodynamic equilibrium as it is for steady nonequilibria working under the condition of local detailed balance. We recover there recently studied "uncertainty" relations for the EP, appearing in studies about the effectiveness of mesoscopic machines. In general our refinement of the positivity of the expected EP rate is obtained in terms of a positive and even function of the expected current(s) which measures the dynamical activity in the system, a time-symmetric estimate of the changes in the system's configuration. Also underdamped diffusions can be included in the analysis.
Conformal Symmetry and Cosmological Entropy Production
Directory of Open Access Journals (Sweden)
Alexander B. Balakin
2002-03-01
Full Text Available Abstract: Introducing an effective refraction index of an isotropic cosmic medium, we investigate the cosmological fluid dynamics which is consistent with a conformal, timelike symmetry of a corresponding "optical" metric. We demonstrate that this kind of symmetry is compatible with the existence of a negative viscous pressure and, consequently, with cosmological entropy production. We establish an exactly solvable model according to which the viscous pressure is a consequence of a self-interacting one-particle force which is self-consistently exerted on the microscopic particles of a relativistic gas. Furthermore, we show that a suficiently high decay rate of the refraction index of an ultrarelativistic cosmic medium results in an in ationary expansion of the universe.
Generalized entropy production fluctuation theorems for quantum ...
Indian Academy of Sciences (India)
rems have helped us in understanding how thermodynamic irreversibility arises ... This is a statement of second law of thermodynamics, expressed in the form of inequality ...... One of the authors (AMJ) thanks DST, India for financial support.
Statistical properties of entropy production derived from fluctuation theorems
International Nuclear Information System (INIS)
Merhav, Neri; Kafri, Yariv
2010-01-01
Several implications of well-known fluctuation theorems, on the statistical properties of entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a given mean of this random variable. It is shown that the Evans–Searles fluctuation theorem alone imposes a significant lower bound on the variance only when the mean entropy production is very small. It is then nonetheless demonstrated that upon incorporating additional information concerning the entropy production, this lower bound can be significantly improved, so as to capture extensivity properties. Another important aspect of the fluctuation properties of the entropy production is the relationship between the mean and the variance, on the one hand, and the probability of the event where the entropy production is negative, on the other hand. Accordingly, we derive upper and lower bounds on this probability in terms of the mean and the variance. These bounds are tighter than previous bounds that can be found in the literature. Moreover, they are tight in the sense that there exist probability distributions, satisfying the Evans–Searles fluctuation theorem, that achieve them with equality. Finally, we present a general method for generating a wide class of inequalities that must be satisfied by the entropy production. We use this method to derive several new inequalities that go beyond the standard derivation of the second law
Fractal Structure and Entropy Production within the Central Nervous System
Directory of Open Access Journals (Sweden)
Andrew J. E. Seely
2014-08-01
Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.
International Nuclear Information System (INIS)
Johannessen, Eivind; Rosjorde, Audun
2007-01-01
We show that the theorem of equipartition of entropy production is important for the understanding of the state of minimum entropy production in diabatic distillation. The theorem is not valid in a strictly mathematical sense. We explain why, when and in what sense this theorem is a good approximation to the optimal state in diabatic distillation. In order to make these predictions, we use a hypothesis for the state of minimum entropy production of an optimally controlled system, which was formulated on the basis of results of entropy production minimisation in chemical reactors. The hypothesis says that the state of minimum entropy production is characterised by approximately constant local entropy production and thermodynamic forces, given that there is sufficient freedom in the system. We present numerical results which are in agreement with the predictions. The results show that a column with constant tray entropy production in the stripping section and in the rectifying section is a good approximation to the optimal column, except when the total heat transfer area is low. The agreement between the two columns becomes better and better as the total heat transfer area and the number of trays increase. The fact that the predictions and the numerical results agree very well gives support to the validity of the hypothesis
di Liberto, Francesco; Pastore, Raffaele; Peruggi, Fulvio
2011-05-01
When some entropy is transferred, by means of a reversible engine, from a hot heat source to a colder one, the maximum efficiency occurs, i.e. the maximum available work is obtained. Similarly, a reversible heat pumps transfer entropy from a cold heat source to a hotter one with the minimum expense of energy. In contrast, if we are faced with non-reversible devices, there is some lost work for heat engines, and some extra work for heat pumps. These quantities are both related to entropy production. The lost work, i.e. ? , is also called 'degraded energy' or 'energy unavailable to do work'. The extra work, i.e. ? , is the excess of work performed on the system in the irreversible process with respect to the reversible one (or the excess of heat given to the hotter source in the irreversible process). Both quantities are analysed in detail and are evaluated for a complex process, i.e. the stepwise circular cycle, which is similar to the stepwise Carnot cycle. The stepwise circular cycle is a cycle performed by means of N small weights, dw, which are first added and then removed from the piston of the vessel containing the gas or vice versa. The work performed by the gas can be found as the increase of the potential energy of the dw's. Each single dw is identified and its increase, i.e. its increase in potential energy, evaluated. In such a way it is found how the energy output of the cycle is distributed among the dw's. The size of the dw's affects entropy production and therefore the lost and extra work. The distribution of increases depends on the chosen removal process.
IRREVERSIBILITY GENERATION IN SUGAR, ALCOHOL AND BIOGAS INTEGRATED PRODUCTIONS
Meilyn González Cortés; Yenisleidy Martínez Martínez; Yailet Albernas Carvajal; Raúl A. Pérez Bermúdez
2017-01-01
In this work, the stages of losses and lower exergetic efficiency are determined when the sugar production process is integrated with others for the production of products such as biogas, torula yeast and electricity. The study is carried out in three scenarios of integrated processes for obtaining the indicated products. A sugar factory in which sugar and electricity are produced is considered as the base scenario and from this; a second scenario is inferred in which alcohol is produced from...
Benfenati, Francesco; Beretta, Gian Paolo
2018-04-01
We show that to prove the Onsager relations using the microscopic time reversibility one necessarily has to make an ergodic hypothesis, or a hypothesis closely linked to that. This is true in all the proofs of the Onsager relations in the literature: from the original proof by Onsager, to more advanced proofs in the context of linear response theory and the theory of Markov processes, to the proof in the context of the kinetic theory of gases. The only three proofs that do not require any kind of ergodic hypothesis are based on additional hypotheses on the macroscopic evolution: Ziegler's maximum entropy production principle (MEPP), the principle of time reversal invariance of the entropy production, or the steepest entropy ascent principle (SEAP).
Institute of Scientific and Technical Information of China (English)
Xie Wen-Xian; Xu Wei; Cai Li
2007-01-01
This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.
International Nuclear Information System (INIS)
Guo Yongfeng; Xu Wei; Li Dongxi; Xie Wenxian
2008-01-01
A stochastic dissipative dynamical system driven by non-Gaussian noise is investigated. A general approximate Fokker-Planck equation of the system is derived through a path-integral approach. Based on the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production of the system is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculation can be used to interpret the interplay of the dissipative constant and non-Gaussian noise on the entropy flux and entropy production
Entropy production in the relativistic heavy ion collisions
International Nuclear Information System (INIS)
Holme, A.K.; Csernai, L.P.; Levai, P.; Papp, G.
1989-09-01
A short overview is given on the most important possibilities of entropy production in the relativistic heavy ion collisions, which is connected to the shock phenomena. The E802 experiment is considered as an example, where one can determine the specific entropy content from measured strange particle ratios. The received large entropy value (S/N B ∼ 14) can be explained by assuming quark-gluon plasma formation. The possibility of overcooling of quark-gluon plasma and its deflagration are also investigated. (author) 22 refs.; 4 figs
Directory of Open Access Journals (Sweden)
Florian Ries
2017-08-01
Full Text Available In the present paper, thermal transport and entropy production mechanisms in a turbulent round jet of compressed nitrogen at supercritical thermodynamic conditions are investigated using a direct numerical simulation. First, thermal transport and its contribution to the mixture formation along with the anisotropy of heat fluxes and temperature scales are examined. Secondly, the entropy production rates during thermofluid processes evolving in the supercritical flow are investigated in order to identify the causes of irreversibilities and to display advantageous locations of handling along with the process regimes favorable to mixing. Thereby, it turned out that (1 the jet disintegration process consists of four main stages under supercritical conditions (potential core, separation, pseudo-boiling, turbulent mixing, (2 causes of irreversibilities are primarily due to heat transport and thermodynamic effects rather than turbulence dynamics and (3 heat fluxes and temperature scales appear anisotropic even at the smallest scales, which implies that anisotropic thermal diffusivity models might be appropriate in the context of both Reynolds-averaged Navier–Stokes (RANS and large eddy simulation (LES approaches while numerically modeling supercritical fluid flows.
Entropy production rate as a criterion for inconsistency in decision theory
Dixit, Purushottam D.
2018-05-01
Individual and group decisions are complex, often involving choosing an apt alternative from a multitude of options. Evaluating pairwise comparisons breaks down such complex decision problems into tractable ones. Pairwise comparison matrices (PCMs) are regularly used to solve multiple-criteria decision-making problems, for example, using Saaty’s analytic hierarchy process (AHP) framework. However, there are two significant drawbacks of using PCMs. First, humans evaluate PCMs in an inconsistent manner. Second, not all entries of a large PCM can be reliably filled by human decision makers. We address these two issues by first establishing a novel connection between PCMs and time-irreversible Markov processes. Specifically, we show that every PCM induces a family of dissipative maximum path entropy random walks (MERW) over the set of alternatives. We show that only ‘consistent’ PCMs correspond to detailed balanced MERWs. We identify the non-equilibrium entropy production in the induced MERWs as a metric of inconsistency of the underlying PCMs. Notably, the entropy production satisfies all of the recently laid out criteria for reasonable consistency indices. We also propose an approach to use incompletely filled PCMs in AHP. Potential future avenues are discussed as well.
Energy conservation and maximal entropy production in enzyme reactions.
Dobovišek, Andrej; Vitas, Marko; Brumen, Milan; Fajmut, Aleš
2017-08-01
A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production. Copyright © 2017 Elsevier B.V. All rights reserved.
Entropy production and plant transpiration in the Liz catchment
Czech Academy of Sciences Publication Activity Database
Šír, Miloslav; Tesař, Miroslav; Krejča, M.; Weger, J.
2008-01-01
Roč. 1, č. 1 (2008), s. 81-89 ISSN 1802-503X Grant - others:MŠMT(CZ) 2B06132 Institutional research plan: CEZ:AV0Z20600510 Keywords : plant transpiration * phytomass productivity * heat balance * entropy production Subject RIV: DA - Hydrology ; Limnology
Entropy production of a Brownian ellipsoid in the overdamped limit.
Marino, Raffaele; Eichhorn, Ralf; Aurell, Erik
2016-01-01
We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.
Minimization of entropy production in separate and connected process units
Energy Technology Data Exchange (ETDEWEB)
Roesjorde, Audun
2004-08-01
The objective of this thesis was to further develop a methodology for minimizing the entropy production of single and connected chemical process units. When chemical process equipment is designed and operated at the lowest entropy production possible, the energy efficiency of the equipment is enhanced. We have found for single process units that the entropy production could be reduced with up to 20-40%, given the degrees of freedom in the optimization. In processes, our results indicated that even bigger reductions were possible. The states of minimum entropy production were studied and important painter's for obtaining significant reductions in the entropy production were identified. Both from sustain ability and economical viewpoints knowledge of energy efficient design and operation are important. In some of the systems we studied, nonequilibrium thermodynamics was used to model the entropy production. In Chapter 2, we gave a brief introduction to different industrial applications of nonequilibrium thermodynamics. The link between local transport phenomena and overall system description makes nonequilibrium thermodynamics a useful tool for understanding design of chemical process units. We developed the methodology of minimization of entropy production in several steps. First, we analyzed and optimized the entropy production of single units: Two alternative concepts of adiabatic distillation; diabatic and heat-integrated distillation, were analyzed and optimized in Chapter 3 to 5. In diabatic distillation, heat exchange is allowed along the column, and it is this feature that increases the energy efficiency of the distillation column. In Chapter 3, we found how a given area of heat transfer should be optimally distributed among the trays in a column separating a mixture of propylene and propane. The results showed that heat exchange was most important on the trays close to the re boiler and condenser. In Chapter 4 and 5, we studied how the entropy
International Nuclear Information System (INIS)
Csernai, L.P.; Lukacs, B.
1984-04-01
In a fluid-dynamical model the extra entropy production is calculated which arises from a non-equilibrium phase transition from nuclear to quark matter. The dynamics of processes producing extra entropy are treated in linear approximation. It is shown that there is a considerable extra entropy production provided the transition is not too fast. In measuring the entropy at the break-up, an excess entropy might signalize the phase transition to a transient quark-gluon plasma. (D.Gy.)
Configurational entropy and ρ and ϕ mesons production in QCD
Karapetyan, G.
2018-06-01
In the present work the electroproduction for diffractive ρ and ϕ mesons by considering AdS/QCD correspondence and Color Glass Condensate (CGC) approximation are studied with respect to the associated dipole cross section, whose parameters are studied and analysed in the framework of the configurational entropy. Our results suggest different quantum states of the nuclear matter, showing that the extremal points of the nuclear configurational entropy is able to reflect a true description of the ρ and ϕ mesons production, using current data concerning light quark masses. During the computations parameters, obtained in fitting procedure, coincide to the experimental within ∼ 0.1%.
Entropy Production and Fluctuation Theorems for Active Matter
Mandal, Dibyendu; Klymko, Katherine; DeWeese, Michael R.
2017-12-01
Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.
Modeling Electric Discharges with Entropy Production Rate Principles
Directory of Open Access Journals (Sweden)
Thomas Christen
2009-12-01
Full Text Available Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production rate principles are related to the maximum entropy production rate principle (MEPP. Secondly, three typical examples are discussed, which provide a certain insight in the structure of the models that are candidates for MEPP application. It is then thirdly argued that MEPP, although not being an exact physical law, may provide reasonable model parameter estimates, provided the constraints contain the relevant (nonlinear physical effects and the parameters to be determined are related to disregarded weak constraints that affect mainly global entropy production. Finally, it is additionally conjectured that a further reason for the success of MEPP in certain far from equilibrium systems might be based on a hidden linearity of the underlying kinetic equation(s.
Fisher-Renyi entropy product and information plane
International Nuclear Information System (INIS)
Romera, E.; Nagy, A.
2008-01-01
Connection between Fisher information and Renyi entropy has been established. This link allows us to define the Fisher-Renyi information plane and an entropic product in terms of these quantities. New Renyi uncertainty relations are obtained for single particle densities of many particle systems in position-momentum conjugate spaces
Minimum entropy production principle from a dynamical fluctuation law
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel
2007-01-01
Roč. 48, č. 5 (2007), 053306/1-053306/12 ISSN 0022-2488 R&D Projects: GA ČR GA202/07/0404 Institutional research plan: CEZ:AV0Z10100520 Keywords : dynamical fluctuations * entropy production Subject RIV: BE - Theoretical Physics Impact factor: 1.137, year: 2007
Directory of Open Access Journals (Sweden)
Hang Liu
2016-08-01
Full Text Available In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions d>4 with at least one rotation parameter ai=0, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions (d>4 and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product but the criterion for angular momentum-independence of entropy product will be affected.
Stochastic thermodynamics and entropy production of chemical reaction systems
Tomé, Tânia; de Oliveira, Mário J.
2018-06-01
We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end, we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of chemical reaction systems based on a master equation defined on the space of microscopic chemical states and on appropriate definitions of entropy and entropy production. The system is in contact with a heat reservoir and is placed out of equilibrium by the contact with particle reservoirs. In our approach, the fluxes of various types, such as the heat and particle fluxes, play a fundamental role in characterizing the nonequilibrium chemical state. We show that the rate of entropy production in the stationary nonequilibrium state is a bilinear form in the affinities and the fluxes of reaction, which are expressed in terms of rate constants and transition rates, respectively. We also show how the description in terms of microscopic states can be reduced to a description in terms of the numbers of particles of each species, from which follows the chemical master equation. As an example, we calculate the rate of entropy production of the first and second Schlögl reaction models.
Entropy production of stationary diffusions on non-compact Riemannian manifolds
Institute of Scientific and Technical Information of China (English)
龚光鲁; 钱敏平
1997-01-01
The closed form of the entropy production of stationary diffusion processes with bounded Nelson’s current velocity is given.The limit of the entropy productions of a sequence of reflecting diffusions is also discussed.
Experimental Rectification of Entropy Production by Maxwell's Demon in a Quantum System
Camati, Patrice A.; Peterson, John P. S.; Batalhão, Tiago B.; Micadei, Kaonan; Souza, Alexandre M.; Sarthour, Roberto S.; Oliveira, Ivan S.; Serra, Roberto M.
2016-12-01
Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1 /2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1 /2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
Entropy, matter, and cosmology.
Prigogine, I; Géhéniau, J
1986-09-01
The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary "C" field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production.
On Thermodynamic Interpretation of Transfer Entropy
Directory of Open Access Journals (Sweden)
Don C. Price
2013-02-01
Full Text Available We propose a thermodynamic interpretation of transfer entropy near equilibrium, using a specialised Boltzmann’s principle. The approach relates conditional probabilities to the probabilities of the corresponding state transitions. This in turn characterises transfer entropy as a difference of two entropy rates: the rate for a resultant transition and another rate for a possibly irreversible transition within the system affected by an additional source. We then show that this difference, the local transfer entropy, is proportional to the external entropy production, possibly due to irreversibility. Near equilibrium, transfer entropy is also interpreted as the difference in equilibrium stabilities with respect to two scenarios: a default case and the case with an additional source. Finally, we demonstrated that such a thermodynamic treatment is not applicable to information flow, a measure of causal effect.
Non-equilibrium Dynamics, Thermalization and Entropy Production
International Nuclear Information System (INIS)
Hinrichsen, Haye; Janotta, Peter; Gogolin, Christian
2011-01-01
This paper addresses fundamental aspects of statistical mechanics such as the motivation of a classical state space with spontaneous transitions, the meaning of non-equilibrium in the context of thermalization, and the justification of these concepts from the quantum-mechanical point of view. After an introductory part we focus on the problem of entropy production in non-equilibrium systems. In particular, the generally accepted formula for entropy production in the environment is analyzed from a critical perspective. It is shown that this formula is only valid in the limit of separated time scales of the system's and the environmental degrees of freedom. Finally, we present an alternative simple proof of the fluctuation theorem.
Application of the maximum entropy production principle to electrical systems
International Nuclear Information System (INIS)
Christen, Thomas
2006-01-01
For a simple class of electrical systems, the principle of the maximum entropy production rate (MaxEP) is discussed. First, we compare the MaxEP principle and the principle of the minimum entropy production rate and illustrate the superiority of the MaxEP principle for the example of two parallel constant resistors. Secondly, we show that the Steenbeck principle for the electric arc as well as the ohmic contact behaviour of space-charge limited conductors follow from the MaxEP principle. In line with work by Dewar, the investigations seem to suggest that the MaxEP principle can also be applied to systems far from equilibrium, provided appropriate information is available that enters the constraints of the optimization problem. Finally, we apply the MaxEP principle to a mesoscopic system and show that the universal conductance quantum, e 2 /h, of a one-dimensional ballistic conductor can be estimated
Irreversibility and conditional probability
International Nuclear Information System (INIS)
Stuart, C.I.J.M.
1989-01-01
The mathematical entropy - unlike physical entropy - is simply a measure of uniformity for probability distributions in general. So understood, conditional entropies have the same logical structure as conditional probabilities. If, as is sometimes supposed, conditional probabilities are time-reversible, then so are conditional entropies and, paradoxically, both then share this symmetry with physical equations of motion. The paradox is, of course that probabilities yield a direction to time both in statistical mechanics and quantum mechanics, while the equations of motion do not. The supposed time-reversibility of both conditionals seems also to involve a form of retrocausality that is related to, but possibly not the same as, that described by Costa de Beaurgard. The retrocausality is paradoxically at odds with the generally presumed irreversibility of the quantum mechanical measurement process. Further paradox emerges if the supposed time-reversibility of the conditionals is linked with the idea that the thermodynamic entropy is the same thing as 'missing information' since this confounds the thermodynamic and mathematical entropies. However, it is shown that irreversibility is a formal consequence of conditional entropies and, hence, of conditional probabilities also. 8 refs. (Author)
Elbert, Donald L; Patterson, Bruce W; Bateman, Randall J
2015-03-01
Amyloid beta (Aβ) peptides, and in particular Aβ42, are found in senile plaques associated with Alzheimer's disease. A compartmental model of Aβ production, exchange and irreversible loss was recently developed to explain the kinetics of isotope-labeling of Aβ peptides collected in cerebrospinal fluid (CSF) following infusion of stable isotope-labeled leucine in humans. The compartmental model allowed calculation of the rates of production, irreversible loss (or turnover) and short-term exchange of Aβ peptides. Exchange of Aβ42 was particularly pronounced in amyloid plaque-bearing participants. In the current work, we describe in much greater detail the characteristics of the compartmental model to two distinct audiences: physician-scientists and biokineticists. For physician-scientists, we describe through examples the types of questions the model can and cannot answer, as well as correct some misunderstandings of previous kinetic analyses applied to this type of isotope labeling data. For biokineticists, we perform a system identifiability analysis and a sensitivity analysis of the kinetic model to explore the global and local properties of the model. Combined, these analyses motivate simplifications from a more comprehensive physiological model to the final model that was previously presented. The analyses clearly demonstrate that the current dataset and compartmental model allow determination with confidence a single 'turnover' parameter, a single 'exchange' parameter and a single 'delay' parameter. When combined with CSF concentration data for the Aβ peptides, production rates may also be obtained. Copyright © 2015 Elsevier Inc. All rights reserved.
Irreversible dynamics, Onsager-Casimir symmetry, and an application to turbulence.
Ottinger, Hans Christian
2014-10-01
Irreversible contributions to the dynamics of nonequilibrium systems can be formulated in terms of dissipative, or irreversible, brackets. We discuss the structure of such irreversible brackets in view of a degeneracy implied by energy conservation, where we consider different types of symmetries of the bracket corresponding to the Onsager and Casimir symmetries of linear irreversible thermodynamics. Slip and turbulence provide important examples of antisymmetric irreversible brackets and offer guidance for the more general modeling of irreversible dynamics without entropy production. Conversely, turbulence modeling could benefit from elucidating thermodynamic structure. The examples suggest constructing antisymmetric irreversible brackets in terms of completely antisymmetric functions of three indices. Irreversible brackets without well-defined symmetry properties can arise for rare events, causing big configurational changes.
Evaluation of the Atmospheric Chemical Entropy Production of Mars
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Alfonso Delgado-Bonal
2015-07-01
Full Text Available Thermodynamic disequilibrium is a necessary situation in a system in which complex emergent structures are created and maintained. It is known that most of the chemical disequilibrium, a particular type of thermodynamic disequilibrium, in Earth’s atmosphere is a consequence of life. We have developed a thermochemical model for the Martian atmosphere to analyze the disequilibrium by chemical reactions calculating the entropy production. It follows from the comparison with the Earth atmosphere that the magnitude of the entropy produced by the recombination reaction forming O3 (O + O2 + CO2 ⥦ O3 + CO2 in the atmosphere of the Earth is larger than the entropy produced by the dominant set of chemical reactions considered for Mars, as a consequence of the low density and the poor variety of species of the Martian atmosphere. If disequilibrium is needed to create and maintain self-organizing structures in a system, we conclude that the current Martian atmosphere is unable to support large physico-chemical structures, such as those created on Earth.
ENTROPY PRODUCTION IN COLLISIONLESS SYSTEMS. I. LARGE PHASE-SPACE OCCUPATION NUMBERS
International Nuclear Information System (INIS)
Barnes, Eric I.; Williams, Liliya L. R.
2011-01-01
Certain thermal non-equilibrium situations, outside of the astrophysical realm, suggest that entropy production extrema, instead of entropy extrema, are related to stationary states. In an effort to better understand the evolution of collisionless self-gravitating systems, we investigate the role of entropy production and develop expressions for the entropy production rate in two particular statistical families that describe self-gravitating systems. From these entropy production descriptions, we derive the requirements for extremizing the entropy production rate in terms of specific forms for the relaxation function in the Boltzmann equation. We discuss some implications of these relaxation functions and point to future work that will further test this novel thermodynamic viewpoint of collisionless relaxation.
Directory of Open Access Journals (Sweden)
Cesare Nardini
2017-04-01
Full Text Available Active-matter systems operate far from equilibrium because of the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: It vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space or spectrally (in Fourier space, allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces, with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wave-vector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics.
Irreversible thermodynamics, parabolic law and self-similar state in grain growth
International Nuclear Information System (INIS)
Rios, P.R.
2004-01-01
The formalism of the thermodynamic theory of irreversible processes is applied to grain growth to investigate the nature of the self-similar state and its corresponding parabolic law. Grain growth does not reach a steady state in the sense that the entropy production remains constant. However, the entropy production can be written as a product of two factors: a scale factor that tends to zero for long times and a scaled entropy production. It is suggested that the parabolic law and the self-similar state may be associated with the minimum of this scaled entropy production. This result implies that the parabolic law and the self-similar state have a sound irreversible thermodynamical basis
Microscopic entropy and nonlocality
International Nuclear Information System (INIS)
Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.
2003-01-01
We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper
Entropy, pricing and productivity of pumped-storage
Karakatsanis, Georgios; Tyralis, Hristos; Tzouka, Katerina
2016-04-01
Pumped-storage constitutes today a mature method of bulk electricity storage in the form of hydropower. This bulk electricity storability upgrades the economic value of hydropower as it may mitigate -or even neutralize- stochastic effects deriving from various geophysical and socioeconomic factors, which produce numerous load balance inefficiencies due to increased uncertainty. Pumped-storage further holds a key role for unifying intermittent renewable (i.e. wind, solar) units with controllable non-renewable (i.e. nuclear, coal) fuel electricity generation plants into integrated energy systems. We develop a set of indicators for the measurement of performance of pumped-storage, in terms of the latter's energy and financial contribution to the energy system. More specifically, we use the concept of entropy in order to examine: (1) the statistical features -and correlations- of the energy system's intermittent components and (2) the statistical features of electricity demand prediction deviations. In this way, the macroeconomics of pumped-storage emerges naturally from its statistical features (Karakatsanis et al. 2014). In addition, these findings are combined to actual daily loads. Hence, not only the amount of energy harvested from the pumped-storage component is expected to be important, but the harvesting time as well, as the intraday price of electricity varies significantly. Additionally, the structure of the pumped-storage market proves to be a significant factor as well for the system's energy and financial performance (Paine et al. 2014). According to the above, we aim at postulating a set of general rules on the productivity of pumped-storage for (integrated) energy systems. Keywords: pumped-storage, storability, economic value of hydropower, stochastic effects, uncertainty, energy systems, entropy, intraday electricity price, productivity References 1. Karakatsanis, Georgios et al. (2014), Entropy, pricing and macroeconomics of pumped-storage systems
Maximum entropy production: Can it be used to constrain conceptual hydrological models?
M.C. Westhoff; E. Zehe
2013-01-01
In recent years, optimality principles have been proposed to constrain hydrological models. The principle of maximum entropy production (MEP) is one of the proposed principles and is subject of this study. It states that a steady state system is organized in such a way that entropy production is maximized. Although successful applications have been reported in...
Constructal theory through thermodynamics of irreversible processes framework
International Nuclear Information System (INIS)
Tescari, S.; Mazet, N.; Neveu, P.
2011-01-01
Highlights: → Point to area flow problem is solved through Thermodynamics of irreversible processes. → A new optimisation criterion is defined: the exergy or entropy impedance. → Optimisation is performed following two different routes, constructal or global. → Global optimisation is more efficient than constructal optimisation. → Global optimisation enhances the domain of construct benefits. - Abstract: Point to volume flow problem is revisited on a thermodynamics of irreversible processes (TIP) basis. The first step consists in evaluating the local entropy production of the system, and deducing from this expression the phenomenological laws. Then, the total entropy production can be simply evaluated. It is demonstrated that total entropy production can be written in a remarkable form: the product of the so-called entropy impedance with the square of the heat flux. As the heat flux is given, optimisation consists in minimising the entropy impedance. It is also shown that minimising entropy impedance minimises the maximum temperature difference. Applied to the elemental volume, this optimisation process leads to a shape factor close to the one already published. For the first construction, the equivalent system is defined as stated by Prigogine: when subjected to the same constraints, two systems are thermodynamically equivalent if their entropy production is equal. Two optimisation routes are then investigated: a global optimisation where all scales are taken into account and the constructal optimisation where the system is optimised scale by scale. In this second case, results are close to Ghodossi's work. When global optimisation is performed, it is demonstrated that conductive paths have to be spread uniformly in the active material (i.e. the number of elemental volumes must go to infinite). Comparing the two routes, global optimisation leads to better performance than constructal optimisation. Moreover, global optimisation enlarges the domain of
Fluctuation theorem for entropy production during effusion of a relativistic ideal gas.
Cleuren, B; Willaert, K; Engel, A; Van den Broeck, C
2008-02-01
The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and antiparticle pair production and annihilation. In both cases, the fluctuation theorem is verified.
International Nuclear Information System (INIS)
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-01-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production
Goswami, Gurupada; Mukherjee, Biswajit; Bag, Bidhan Chandra
2005-06-01
We have studied the relaxation of non-Markovian and thermodynamically closed system both in the absence and presence of non-equilibrium constraint in terms of the information entropy flux and entropy production based on the Fokker-Planck and the entropy balance equations. Our calculation shows how the relaxation time depends on noise correlation time. It also considers how the non-equilibrium constraint is affected by system parameters such as noise correlation time, strength of dissipation and frequency of dynamical system. The interplay of non-equilibrium constraint, frictional memory kernel, noise correlation time and frequency of dynamical system reveals the extremum nature of the entropy production.
Measures of thermodynamic irreversibility in deterministic and stochastic dynamics
International Nuclear Information System (INIS)
Ford, Ian J
2015-01-01
It is generally observed that if a dynamical system is sufficiently complex, then as time progresses it will share out energy and other properties amongst its component parts to eliminate any initial imbalances, retaining only fluctuations. This is known as energy dissipation and it is closely associated with the concept of thermodynamic irreversibility, measured by the increase in entropy according to the second law. It is of interest to quantify such behaviour from a dynamical rather than a thermodynamic perspective and to this end stochastic entropy production and the time-integrated dissipation function have been introduced as analogous measures of irreversibility, principally for stochastic and deterministic dynamics, respectively. We seek to compare these measures. First we modify the dissipation function to allow it to measure irreversibility in situations where the initial probability density function (pdf) of the system is asymmetric as well as symmetric in velocity. We propose that it tests for failure of what we call the obversibility of the system, to be contrasted with reversibility, the failure of which is assessed by stochastic entropy production. We note that the essential difference between stochastic entropy production and the time-integrated modified dissipation function lies in the sequence of procedures undertaken in the associated tests of irreversibility. We argue that an assumed symmetry of the initial pdf with respect to velocity inversion (within a framework of deterministic dynamics) can be incompatible with the Past Hypothesis, according to which there should be a statistical distinction between the behaviour of certain properties of an isolated system as it evolves into the far future and the remote past. Imposing symmetry on a velocity distribution is acceptable for many applications of statistical physics, but can introduce difficulties when discussing irreversible behaviour. (paper)
Multifield stochastic particle production: beyond a maximum entropy ansatz
Energy Technology Data Exchange (ETDEWEB)
Amin, Mustafa A.; Garcia, Marcos A.G.; Xie, Hong-Yi; Wen, Osmond, E-mail: mustafa.a.amin@gmail.com, E-mail: marcos.garcia@rice.edu, E-mail: hxie39@wisc.edu, E-mail: ow4@rice.edu [Physics and Astronomy Department, Rice University, 6100 Main Street, Houston, TX 77005 (United States)
2017-09-01
We explore non-adiabatic particle production for N {sub f} coupled scalar fields in a time-dependent background with stochastically varying effective masses, cross-couplings and intervals between interactions. Under the assumption of weak scattering per interaction, we provide a framework for calculating the typical particle production rates after a large number of interactions. After setting up the framework, for analytic tractability, we consider interactions (effective masses and cross couplings) characterized by series of Dirac-delta functions in time with amplitudes and locations drawn from different distributions. Without assuming that the fields are statistically equivalent, we present closed form results (up to quadratures) for the asymptotic particle production rates for the N {sub f}=1 and N {sub f}=2 cases. We also present results for the general N {sub f} >2 case, but with more restrictive assumptions. We find agreement between our analytic results and direct numerical calculations of the total occupation number of the produced particles, with departures that can be explained in terms of violation of our assumptions. We elucidate the precise connection between the maximum entropy ansatz (MEA) used in Amin and Baumann (2015) and the underlying statistical distribution of the self and cross couplings. We provide and justify a simple to use (MEA-inspired) expression for the particle production rate, which agrees with our more detailed treatment when the parameters characterizing the effective mass and cross-couplings between fields are all comparable to each other. However, deviations are seen when some parameters differ significantly from others. We show that such deviations become negligible for a broad range of parameters when N {sub f}>> 1.
Local Entropy Production in Turbulent Shear Flows: A Tool for Evaluating Heat Transfer Performance
Institute of Scientific and Technical Information of China (English)
H. HERWIG; F. KOCK
2006-01-01
Performance evaluation of heat transfer devices can be based on the overall entropy production in these devices.In our study we therefore provide equations for the systematic and detailed determination of local entropy production due to dissipation of mechanical energy and due to heat conduction, both in turbulent flows. After turbulence modeling has been incorporated for the fluctuating parts the overall entropy production can be determined by integration with respect to the whole flow domain. Since, however, entropy production rates show very steep gradients close to the wall, numerical solutions are far more effective with wall functions for the entropy production terms. These wall functions are mandatory when high Reynolds number turbulence models are used. For turbulent flow in a pipe with an inserted twisted tape as heat transfer promoter it is shown that based on the overall entropy production rate a clear statement from a thermodynamic point of view is possible. For a certain range of twist strength there is a decrease in overall entropy production compared to the case without insert. Also, the optimum twist strength can be determined. This information is unavailable when only pressure drop and heat transfer data are given.
Sadeghi Ghuchani, Mostafa
2018-02-08
This comment argues against the view that cancer cells produce less entropy than normal cells as stated in a recent paper by Marín and Sabater. The basic principle of estimation of entropy production rate in a living cell is discussed, emphasizing the fact that entropy production depends on both the amount of heat exchange during the metabolism and the entropy difference between products and substrates.
Sadeghi Ghuchani, Mostafa
2018-03-01
This comment argues against the view that cancer cells produce less entropy than normal cells as stated in a recent paper by Marín and Sabater. The basic principle of estimation of entropy production rate in a living cell is discussed, emphasizing the fact that entropy production depends on both the amount of heat exchange during the metabolism and the entropy difference between products and substrates.
The mechanics of granitoid systems and maximum entropy production rates.
Hobbs, Bruce E; Ord, Alison
2010-01-13
A model for the formation of granitoid systems is developed involving melt production spatially below a rising isotherm that defines melt initiation. Production of the melt volumes necessary to form granitoid complexes within 10(4)-10(7) years demands control of the isotherm velocity by melt advection. This velocity is one control on the melt flux generated spatially just above the melt isotherm, which is the control valve for the behaviour of the complete granitoid system. Melt transport occurs in conduits initiated as sheets or tubes comprising melt inclusions arising from Gurson-Tvergaard constitutive behaviour. Such conduits appear as leucosomes parallel to lineations and foliations, and ductile and brittle dykes. The melt flux generated at the melt isotherm controls the position of the melt solidus isotherm and hence the physical height of the Transport/Emplacement Zone. A conduit width-selection process, driven by changes in melt viscosity and constitutive behaviour, operates within the Transport Zone to progressively increase the width of apertures upwards. Melt can also be driven horizontally by gradients in topography; these horizontal fluxes can be similar in magnitude to vertical fluxes. Fluxes induced by deformation can compete with both buoyancy and topographic-driven flow over all length scales and results locally in transient 'ponds' of melt. Pluton emplacement is controlled by the transition in constitutive behaviour of the melt/magma from elastic-viscous at high temperatures to elastic-plastic-viscous approaching the melt solidus enabling finite thickness plutons to develop. The system involves coupled feedback processes that grow at the expense of heat supplied to the system and compete with melt advection. The result is that limits are placed on the size and time scale of the system. Optimal characteristics of the system coincide with a state of maximum entropy production rate. This journal is © 2010 The Royal Society
Rényi-Fisher entropy product as a marker of topological phase transitions
Bolívar, J. C.; Nagy, Ágnes; Romera, Elvira
2018-05-01
The combined Rényi-Fisher entropy product of electrons plus holes displays a minimum at the charge neutrality points. The Stam-Rényi difference and the Stam-Rényi uncertainty product of the electrons plus holes, show maxima at the charge neutrality points. Topological quantum numbers capable of detecting the topological insulator and the band insulator phases, are defined. Upper and lower bounds for the position and momentum space Rényi-Fisher entropy products are derived.
Institute of Scientific and Technical Information of China (English)
吴金平
1991-01-01
The relation between the excess entropy production criterion of thermodynamic stabilityfor nonequilibrium states and kinetic linear stability principle is discussed. It is shown thatthe condition required by the excess entropy production criterion generally is sufficient, butnot necessary to judge the system stability. The condition required by the excess entropyproduction criterion is stronger than that of the linear stability principle. Only when theproduct matrix between the linearized matrix of kinetic equations and matrix of quadraticform of second-order excess entropy is symmetric, is the condition required by the excessentropy production criterion that the steady steate is asymptotically stable (δ_xP>0) necessaryand sufficient. The counterexample given by Fox to prove that the excess entropy, (δ~2S)ss,is not a Liapunov function is incorrect. Contradictory to his conclusion, the counterexampleis just a positive one that proves that the excess entropy is a Liapunov function. Moreover,the excess entropy production criterion is not limited by symmetric conditions of the linear-ized matrix of kinetic equations. The excess entropy around nonequilibrium steady states,(δ~2S)ss, is a Liapunov function of thermodynamic system.
Use and validity of principles of extremum of entropy production in the study of complex systems
International Nuclear Information System (INIS)
Heitor Reis, A.
2014-01-01
It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented. -- Highlights: •The principles of extremum of entropy production are not first principles. •They result from the maximization of conductivities under appropriate constraints. •The conditions of their validity are set explicitly. •Some long-standing controversies are discussed and clarified
Work and entropy production in generalised Gibbs ensembles
International Nuclear Information System (INIS)
Perarnau-Llobet, Martí; Riera, Arnau; Gallego, Rodrigo; Wilming, Henrik; Eisert, Jens
2016-01-01
Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble, reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium. (paper)
Entropy production analysis of hysteresis characteristic of a pump-turbine model
International Nuclear Information System (INIS)
Li, Deyou; Wang, Hongjie; Qin, Yonglin; Han, Lei; Wei, Xianzhu; Qin, Daqing
2017-01-01
Highlights: • An interesting hysteresis phenomenon was analyzed using entropy production theory. • A function was used to calculate the entropy production in the wall region. • Generation mechanism of the hump and hysteresis characteristics was obtained. - Abstract: The hydraulic loss due to friction and unstable flow patterns in hydro-turbines causes a drop in their efficiency. The traditional method for analyzing the hydraulic loss is by evaluating the pressure drop, which has certain limitations and cannot determine the exact locations at which the high hydraulic loss occurs. In this study, entropy production theory was adopted to obtain a detailed distribution of the hydraulic loss in a pump-turbine in the pump mode. In the past, the wall effects of entropy production were not considered, which caused larger errors as compared with the method of pressure difference. First, a wall equation was proposed to calculate the hydraulic loss in the wall region. The comparison of hydraulic loss calculated by entropy production and pressure difference revealed a better result. Then, through the use of the entropy production theory, the performance characteristics were determined for a pump-turbine with 19 mm guide vane opening, and the variation in the entropy production was obtained. Recently, an interesting phenomenon, i.e., a hysteresis characteristic, was observed in the hump region in pump-turbines. Research shows that the hysteresis characteristic is a result of the Euler momentum and hydraulic loss; the hydraulic loss accounts for a major portion of the hysteresis characteristic. Finally, the hysteresis characteristic in the hump region was analyzed in detail through the entropy production. The results showed that the hump characteristic and the accompanying hysteresis phenomenon are caused by backflow at the runner inlet and the presence of separation vortices close to the hub and the shroud in the stay/guide vanes, which is dependent on the direction of
Irreversibility and Action of the Heat Conduction Process
Directory of Open Access Journals (Sweden)
Yu-Chao Hua
2018-03-01
Full Text Available Irreversibility (that is, the “one-sidedness” of time of a physical process can be characterized by using Lyapunov functions in the modern theory of stability. In this theoretical framework, entropy and its production rate have been generally regarded as Lyapunov functions in order to measure the irreversibility of various physical processes. In fact, the Lyapunov function is not always unique. In the represent work, a rigorous proof is given that the entransy and its dissipation rate can also serve as Lyapunov functions associated with the irreversibility of the heat conduction process without the conversion between heat and work. In addition, the variation of the entransy dissipation rate can lead to Fourier’s heat conduction law, while the entropy production rate cannot. This shows that the entransy dissipation rate, rather than the entropy production rate, is the unique action for the heat conduction process, and can be used to establish the finite element method for the approximate solution of heat conduction problems and the optimization of heat transfer processes.
ENTROPY PRODUCTION IN COLLISIONLESS SYSTEMS. II. ARBITRARY PHASE-SPACE OCCUPATION NUMBERS
International Nuclear Information System (INIS)
Barnes, Eric I.; Williams, Liliya L. R.
2012-01-01
We present an analysis of two thermodynamic techniques for determining equilibria of self-gravitating systems. One is the Lynden-Bell (LB) entropy maximization analysis that introduced violent relaxation. Since we do not use the Stirling approximation, which is invalid at small occupation numbers, our systems have finite mass, unlike LB's isothermal spheres. (Instead of Stirling, we utilize a very accurate smooth approximation for ln x!.) The second analysis extends entropy production extremization to self-gravitating systems, also without the use of the Stirling approximation. In addition to the LB statistical family characterized by the exclusion principle in phase space, and designed to treat collisionless systems, we also apply the two approaches to the Maxwell-Boltzmann (MB) families, which have no exclusion principle and hence represent collisional systems. We implicitly assume that all of the phase space is equally accessible. We derive entropy production expressions for both families and give the extremum conditions for entropy production. Surprisingly, our analysis indicates that extremizing entropy production rate results in systems that have maximum entropy, in both LB and MB statistics. In other words, both thermodynamic approaches lead to the same equilibrium structures.
Revisiting the Glansdorff–Prigogine criterion for stability within irreversible thermodynamics
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel
2015-01-01
Roč. 159, č. 6 (2015), s. 1286-1299 ISSN 0022-4715 R&D Projects: GA ČR GAP204/12/0897 Institutional support: RVO:68378271 Keywords : irreversible processes * thermodynamic stability * excess entropy production * nonequilibrium free energy * Clausius heat theorem Subject RIV: BE - Theoretical Physics Impact factor: 1.537, year: 2015
Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels
Directory of Open Access Journals (Sweden)
Benoît Collins
2010-06-01
Full Text Available Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.
From 0 to 5000 in 2 x 10-24 seconds: Entropy production in relativistic heavy-ion collisions
International Nuclear Information System (INIS)
Fries, R.J.; Kunihiro, T.; Mueller, B.; Ohnishi, A.; Schaefer, A.
2009-01-01
We review what is known about the contributions to the final entropy from the different stages of a relativistic nuclear collision, including recent results on the decoherence entropy and the entropy produced during the hydrodynamic phase by viscous effects. We then present a general framework, based on the Husimi distribution function, for the calculation of entropy growth in quantum field theories, which is applicable to the earliest ('glasma') phase of the collision during which most of the entropy is generated. The entropy calculated from the Husimi distribution exhibits linear growth when the quantum field contains unstable modes and is asymptotically equal to the Kolmogorov-Sinai (KS) entropy. We outline how the approach can be used to investigate the problem of entropy production in a relativistic heavy-ion reaction from first principles.
From 0 to 5000 in 2 × 10−24 seconds: Entropy production in relativistic heavy-ion collisions
Energy Technology Data Exchange (ETDEWEB)
Fries, R.; Kunihiro, T.; Muller, B.; Ohnishi, A.; Schafer, A.
2009-11-01
We review what is known about the contributions to the final entropy from the different stages of a relativistic nuclear collision, including recent results on the decoherence entropy and the entropy produced during the hydrodynamic phase by viscous effects. We then present a general framework, based on the Husimi distribution function, for the calculation of entropy growth in quantum field theories, which is applicable to the earliest ('glasma') phase of the collision during which most of the entropy is generated. The entropy calculated from the Husimi distribution exhibits linear growth when the quantum field contains unstable modes and is asymptotically equal to the Kolmogorov-Sinai (KS) entropy. We outline how the approach can be used to investigate the problem of entropy production in a relativistic heavy-ion reaction from first principles.
Entropy production and thermodynamics of nonequilibrium stationary states: a point of view.
Gallavotti, Giovanni
2004-09-01
Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called "caloric") in transformations that are not isochoric (i.e., which involve mechanical work): it could be just a quantity that can be transferred or created, like heat in equilibrium. The text first reviews the philosophy behind a recently proposed definition of entropy production in nonequilibrium stationary systems. A detailed technical attempt at defining the entropy of a stationary states via their variational properties follows: the unsatisfactory aspects of the results add arguments in favor of the nonexistence of a function of state to be identified with entropy; at the same time new aspects and properties of the phase space contraction emerge. Copyright 2004 American Institute of Physics
Entropy Production in Pipeline Flow of Dispersions of Water in Oil
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Rajinder Pal
2014-08-01
Full Text Available Entropy production in pipeline adiabatic flow of water-in-oil emulsions is investigated experimentally in three different diameter pipes. The dispersed-phase (water droplets concentration of emulsion is varied from 0 to 41% vol. The entropy production rates in emulsion flow are compared with the values expected in single-phase flow of Newtonian fluids with the same properties (viscosity and density. While in the laminar regime the entropy production rates in emulsion flow can be described adequately by the single-phase Newtonian equations, a significant deviation from single-phase flow behavior is observed in the turbulent regime. In the turbulent regime, the entropy production rates in emulsion flow are found to be substantially smaller than those expected on the basis of single-phase equations. For example, the entropy production rate in water-in-oil emulsion flow at a dispersed-phase volume fraction of 0.41 is only 38.4% of that observed in flow of a single-phase Newtonian fluid with the same viscosity and density, when comparison is made at a Reynolds number of 4000. Thus emulsion flow in pipelines is more efficient thermodynamically than single-phase Newtonian flow.
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J. J. Vallino
2011-06-01
Full Text Available In this manuscript we investigate the use of the maximum entropy production (MEP principle for modeling biogeochemical processes that are catalyzed by living systems. Because of novelties introduced by the MEP approach, many questions need to be answered and techniques developed in the application of MEP to describe biological systems that are responsible for energy and mass transformations on a planetary scale. In previous work we introduce the importance of integrating entropy production over time to distinguish abiotic from biotic processes under transient conditions. Here we investigate the ramifications of modeling biological systems involving one or more spatial dimensions. When modeling systems over space, entropy production can be maximized either locally at each point in space asynchronously or globally over the system domain synchronously. We use a simple two-box model inspired by two-layer ocean models to illustrate the differences in local versus global entropy maximization. Synthesis and oxidation of biological structure is modeled using two autocatalytic reactions that account for changes in community kinetics using a single parameter each. Our results show that entropy production can be increased if maximized over the system domain rather than locally, which has important implications regarding how biological systems organize and supports the hypothesis for multiple levels of selection and cooperation in biology for the dissipation of free energy.
Fluctuation theorem for entropy production during effusion of a relativistic ideal gas
CLEUREN, Bart; WILLAERT, Koen; ENGEL, Andreas; VAN DEN BROECK, Christian
2008-01-01
The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and anti-particle pair production and annihilation. In both cases, the fluctuation theorem is verified.
Entropy Production and the Pressure-Volume Curve of the Lung
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Cláudio Lucas Oliveira
2016-03-01
Full Text Available We investigate analytically the production of entropy during a breathing cycle in healthy and diseased lungs. First, we calculate entropy production in healthy lungs by applying the laws of thermodynamics to the well-known transpulmonary pressure-volume (P-V curves of the lung under the assumption that lung tissue behaves as an entropy spring-like rubber. The bulk modulus, $B$, of the lung is also derived from these calculations. Second, we extend this approach to elastic recoil disorders of the lung such as occur in pulmonary fibrosis and emphysema. These diseases are characterized by particular alterations in the P-V relationship. For example, in fibrotic lungs B increases monotonically with disease progression, while in emphysema the opposite occurs. These diseases can thus be mimicked simply by making appropriate adjustments to the parameters of the P-V curve. Using Clausius's formalism, we show that entropy production, Delta_S, is related to the hysteresis area, Delta_A, enclosed by the P-V curve during a breathing cycle, namely, Delta_S = Delta_A/T, where T is the body temperature. Although Delta_A is highly dependent on the disease, such formula applies to healthy as well as diseased lungs, regardless of the disease stage. Finally, we use ansatzs to predict analytically the entropy produced by the fibrotic and emphysematous lungs.
Entropy production by Q-ball decay for diluting long-lived charged particles
International Nuclear Information System (INIS)
Kasuya, S.
2007-09-01
The cosmic abundance of a long-lived charged particle such as a stau is tightly constrained by the catalyzed big bang nucleosynthesis. One of the ways to evade the constraints is to dilute those particles by a huge entropy production. We evaluate the dilution factor in a case that non-relativistic matter dominates the energy density of the universe and decays with large entropy production. We find that large Q balls can do the job, which is naturally produced in the gauge-mediated supersymmetry breaking scenario. (orig.)
CFT and Logarithmic Corrections to the Black Hole Entropy Product Formula
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Parthapratim Pradhan
2017-01-01
Full Text Available We examine the logarithmic corrections to the black hole (BH entropy product formula of outer horizon and inner horizon by taking into account the effects of statistical quantum fluctuations around the thermal equilibrium and via conformal field theory (CFT. We argue that, in logarithmic corrections to the BH entropy product formula when calculated using CFT and taking into account the effects of quantum fluctuations around the thermal equilibrium, the formula should not be universal and it also should not be quantized. These results have been explicitly checked by giving several examples.
Beyond the second law entropy production and non-equilibrium systems
Lineweaver, Charles; Niven, Robert; Regenauer-Lieb, Klaus
2014-01-01
The Second Law, a cornerstone of thermodynamics, governs the average direction of dissipative, non-equilibrium processes. But it says nothing about their actual rates or the probability of fluctuations about the average. This interdisciplinary book, written and peer-reviewed by international experts, presents recent advances in the search for new non-equilibrium principles beyond the Second Law, and their applications to a wide range of systems across physics, chemistry and biology. Beyond The Second Law brings together traditionally isolated areas of non-equilibrium research and highlights potentially fruitful connections between them, with entropy production playing the unifying role. Key theoretical concepts include the Maximum Entropy Production principle, the Fluctuation Theorem, and the Maximum Entropy method of statistical inference. Applications of these principles are illustrated in such diverse fields as climatology, cosmology, crystal growth morphology, Earth system science, environmental physics, ...
Physical entropy, information entropy and their evolution equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.
On the validity of entropy production principles for linear electrical circuits
Czech Academy of Sciences Publication Activity Database
Bruers, S.; Maes, C.; Netočný, Karel
2007-01-01
Roč. 129, - (2007), s. 725-740 ISSN 0022-4715 R&D Projects: GA ČR GA202/07/0404 Institutional research plan: CEZ:AV0Z10100520 Keywords : entropy production * variational principles * nonequilibrium fluctuations Subject RIV: BE - Theoretical Physics Impact factor: 1.605, year: 2007
International Nuclear Information System (INIS)
Sun Fengrui; Qin Xiaoyong; Chen Lingen; Wu Chih
2005-01-01
For an endoreversible four-heat-reservoir absorption heat-transformer cycle, for which a linear (Newtonian) heat-transfer law applies, an ecological optimization criterion is proposed for the best mode of operation of the cycle. This involves maximizing a function representing the compromise between the heating load and the entropy-production rate. The optimal relation between the ecological criterion and the COP (coefficient of performance), the maximum ecological criterion and the corresponding COP, heating load and entropy production rate, as well as the ecological criterion and entropy-production rate at the maximum heating load are derived using finite-time thermodynamics. Moreover, compared with the heating-load criterion, the effects of the cycle parameters on the ecological performance are studied by numerical examples. These show that achieving the maximum ecological criterion makes the entropy-production rate decrease by 77.0% and the COP increase by 55.4% with only 27.3% heating-load losses compared with the maximum heating-load objective. The results reflect that the ecological criterion has long-term significance for optimal design of absorption heat-transformers
Expansion, thermalization, and entropy production in high-energy nuclear collisions
International Nuclear Information System (INIS)
Heiselberg, H.; Wang, X.
1996-01-01
The thermalization process is studied in an expanding parton gas using the Boltzmann equation with two types of collision terms. In the relaxation time approximation we determine the criteria under which a time-dependent relaxation time leads to thermalization of the partons. We calculate the entropy production due to collisions for the general time-dependent relaxation time. In a perturbative QCD approach on the other hand, we can, given the initial conditions, estimate the effective relaxation time due to elastic collisions; this will be an upper limit only since radiative processes will also contribute to thermalization. We find that the parton gas does thermalize eventually but only after having undergone a phase of free streaming and gradual equilibration where considerable entropy is produced (open-quote open-quote after burning close-quote close-quote). The final entropy and thus particle density depends on the collision time as well as the initial conditions (a open-quote open-quote memory effect close-quote close-quote). Results for entropy production are presented based upon various model estimates of early parton production. copyright 1996 The American Physical Society
Minimizing the entropy production in a chemical process for dehydrogenation of propane
International Nuclear Information System (INIS)
Rosjorde, A.; Kjelstrup, S.; Johannessen, E.; Hansen, R.
2007-01-01
We minimize the total entropy production of a process designed for dehydrogenation of propane. The process consists of 21 units, including a plug-flow reactor, a partial condenser, two tray distillation columns and a handful of heat exchangers and compressors. The units were modeled in a manner that made them relatively insensitive to changes in the molar flow rates, to make the optimization more flexible. The operating conditions, as well as to some degree the design of selected units, which minimized the total entropy production of the process, were found. The most important variables were the amount of recycled propane and propylene, conversion and selectivity in the reactor, as well as the number of tubes in the reactor. The optimal conversion, selectivity and recycle flows were results of a very clear trade-off among the entropy produced in the reactor, the partial condenser and the two distillation columns. Although several simplifying assumptions were made for computational reasons, this shows for the first time that it is also meaningful to use the entropy production as an objective function in chemical engineering process optimization studies
Entropy production and multiple equilibria: the case of the ice-albedo feedback
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C. Herbert
2011-02-01
Full Text Available Nonlinear feedbacks in the Earth System provide mechanisms that can prove very useful in understanding complex dynamics with relatively simple concepts. For example, the temperature and the ice cover of the planet are linked in a positive feedback which gives birth to multiple equilibria for some values of the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate unstable solution. In this study, we show an analogy between a classical dynamical system approach to this problem and a Maximum Entropy Production (MEP principle view, and we suggest a glimpse on how to reconcile MEP with the time evolution of a variable. It enables us in particular to resolve the question of the stability of the entropy production maxima. We also compare the surface heat flux obtained with MEP and with the bulk-aerodynamic formula.
Entropy production and rectification efficiency in colloid transport along a pulsating channel
Florencia Carusela, M.; Rubi, J. Miguel
2018-06-01
We study the current rectification of particles moving in a pulsating channel under the influence of an applied force. We have shown the existence of different rectification scenarios in which entropic and energetic effects compete. The effect can be quantified by means of a rectification coefficient that is analyzed in terms of the force, the frequency and the diffusion coefficient. The energetic cost of the motion of the particles expressed in terms of the entropy production depends on the importance of the entropic contribution to the total force. Rectification is more important at low values of the applied force when entropic effects become dominant. In this regime, the entropy production is not invariant under reversal of the applied force. The phenomenon observed could be used to optimize transport in microfluidic devices or in biological channels.
Comments on a derivation and application of the 'maximum entropy production' principle
International Nuclear Information System (INIS)
Grinstein, G; Linsker, R
2007-01-01
We show that (1) an error invalidates the derivation (Dewar 2005 J. Phys. A: Math. Gen. 38 L371) of the maximum entropy production (MaxEP) principle for systems far from equilibrium, for which the constitutive relations are nonlinear; and (2) the claim (Dewar 2003 J. Phys. A: Math. Gen. 36 631) that the phenomenon of 'self-organized criticality' is a consequence of MaxEP for slowly driven systems is unjustified. (comment)
Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer.
Wood, Kevin; Van den Broeck, C; Kawai, R; Lindenberg, Katja
2007-06-01
We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Cleuren [Phys. Rev. E 74, 021117 (2006)], we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.
Non-equilibrium Thermodynamics and the Production of Entropy Life, Earth, and Beyond
Kleidon, Axel
2005-01-01
The present volume studies the application of concepts from non-equilibrium thermodynamics to a variety of research topics. Emphasis is on the Maximum Entropy Production (MEP) principle and applications to Geosphere-Biosphere couplings. Written by leading researchers form a wide range of background, the book proposed to give a first coherent account of an emerging field at the interface of thermodynamics, geophysics and life sciences.
Energy consumption and entropy production in a stochastic formulation of BCM learning
International Nuclear Information System (INIS)
De Oliveira, L R; Castellani, G; Turchetti, G
2013-01-01
Biochemical processes in living cells are open systems, therefore they exchange materials with their environment and they consume chemical energy. These processes are molecular-based and for that reason the role of fluctuations can not be ignored and the stochastic description is the most appropriate one. The chemical master equation describes in exact way the probabilistic dynamics of a given discrete set of states and helps us to understand and clarify the differences between closed and open systems. A closed system is related to a condition of detailed balance (DB), i.e. an equilibrium state. After a sufficiently long period, an open system will reach a non-equilibrium steady state (NESS) that is sustained by a flux of external energy. We demonstrate that two implementations of the BCM learning rule (BCM82) and (BCM92) are, respectively, always in DB, and never in DB. We define a one parameter parametrization of the BCM learning rule that interpolates between these two extremes. We compute thermodynamical quantities such as internal energy, free energy (both Helmholtz and Gibbs) and entropy. The entropy variation in the case of open systems (i.e. when DB does not hold) can be divided into internal entropy production and entropy exchanged with surroundings. We show how the entropy variation can be used to find the optimal value (corresponding to increased robustness and stability) for the parameter used in the BCM parametrization. Finally, we use the calculation of the work to drive the system from an initial state to the steady state as the parameter of the plasticity of the system
On extremals of the entropy production by ‘Langevin–Kramers’ dynamics
International Nuclear Information System (INIS)
Muratore-Ginanneschi, Paolo
2014-01-01
We refer as ‘Langevin–Kramers’ dynamics to a class of stochastic differential systems exhibiting a degenerate ‘metriplectic’ structure. This means that the drift field can be decomposed into a symplectic and a gradient-like component with respect to a pseudo-metric tensor associated with random fluctuations affecting increments of only a sub-set of the degrees of freedom. Systems in this class are often encountered in applications as elementary models of Hamiltonian dynamics in a heat bath eventually relaxing to a Boltzmann steady state. Entropy production control in Langevin–Kramers models differs from the now well-understood case of Langevin–Smoluchowski dynamics for two reasons. First, the definition of entropy production stemming from fluctuation theorems specifies a cost functional which does not act coercively on all degrees of freedom of control protocols. Second, the presence of a symplectic structure imposes a non-local constraint on the class of admissible controls. Using Pontryagin control theory and restricting the attention to additive noise, we show that smooth protocols attaining extremal values of the entropy production appear generically in continuous parametric families as a consequence of a trade-off between smoothness of the admissible protocols and non-coercivity of the cost functional. Uniqueness is, however, always recovered in the over-damped limit as extremal equations reduce at leading order to the Monge–Ampère–Kantorovich optimal mass-transport equations. (paper)
Directory of Open Access Journals (Sweden)
Brohi Ali Anwar
2017-01-01
Full Text Available The entropy production in 2-D heat transfer system has been analyzed systematically by using the finite volume method, to develop new criteria for the numerical simulation in case of multidimensional systems, with the aid of the CFD codes. The steady-state heat conduction problem has been investigated for entropy production, and the entropy production profile has been calculated based upon the current approach. From results for 2-D heat conduction, it can be found that the stability of entropy production profile exhibits a better agreement with the exact solution accordingly, and the current approach is effective for measuring the accuracy and stability of numerical simulations for heat transfer problems.
Bellan, J.; Okongo, N.
2000-01-01
A study of emerging turbulent scales entropy production is conducted for a supercritical shear layer as a precursor to the eventual modeling of Subgrid Scales (from a turbulent state) leading to Large Eddy Simulations.
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S. Pascale
2012-01-01
Full Text Available The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m^{−2} K^{−1} of material entropy production is due to vertical heat transport and 5–7 mW m^{−2} K^{−1} to horizontal heat transport.
Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection
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Stuart Bartlett
2016-12-01
Full Text Available Multiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP. However, almost all such investigations were limited to fixed temperature boundary conditions (BCs. It was found that under those conditions, the system tends to maximize its heat flux, and hence it was concluded that the MEP state is a dynamical attractor. However, since entropy production varies with heat flux and difference of inverse temperature, it is essential that any complete investigation of entropy production allows for variations in heat flux and temperature difference. Only then can we legitimately assess whether the MEP state is the most attractive. Our previous work made use of negative feedback BCs to explore this possibility. We found that the steady state of the system was far from the MEP state. For any system, entropy production can only be maximized subject to a finite set of physical and material constraints. In the case of our previous work, it was possible that the adopted set of fluid parameters were constraining the system in such a way that it was entirely prevented from reaching the MEP state. Hence, in the present work, we used a different set of boundary parameters, such that the steady states of the system were in the local vicinity of the MEP state. If MEP was indeed an attractor, relaxing those constraints of our previous work should have caused a discrete perturbation to the surface of steady state heat flux values near the value corresponding to MEP. We found no such perturbation, and hence no discernible attraction to the MEP state. Furthermore, systems with fixed flux BCs actually minimize their entropy production (relative to the alternative stable state, that of pure diffusive heat transport. This leads us to conclude that the principle of MEP is not an accurate indicator of which stable steady state a convective system will adopt. However, for all BCs considered, the quotient of
Entropy Production and Equilibrium Conditions of General-Covariant Spin Systems
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Wolfgang Muschik
2015-12-01
Full Text Available In generalizing the special-relativistic one-component version of Eckart’s continuum thermodynamics to general-relativistic space-times with Riemannian or post-Riemannian geometry as presented by Schouten (Schouten, J.A. Ricci-Calculus, 1954 and Blagojevic (Blagojevic, M. Gauge Theories of Gravitation, 2013 we consider the entropy production and other thermodynamical quantities, such as the entropy flux and the Gibbs fundamental equation. We discuss equilibrium conditions in gravitational theories, which are based on such geometries. In particular, thermodynamic implications of the non-symmetry of the energy-momentum tensor and the related spin balance equations are investigated, also for the special case of general relativity.
Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer
International Nuclear Information System (INIS)
Christen, Thomas; Kassubek, Frank
2009-01-01
In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and (generally nongrey) matter. The method provides the nonequilibrium photon distribution from which the effective (variable) absorption coefficients and the variable Eddington factor (VEF) can be calculated. For a single band model, the photon distribution depends explicitly on the frequency dependence of the absorption coefficient. Without introducing artificial fit parameters, multi-group or multi-band concepts, our approach reproduces the exact results in both limits of optically thick (Rosseland mean) and optically thin (Planck mean) media, in contrast to the maximum entropy method. Also the results for general nonequilibrium radiation between the limits of diffusive and ballistic photons are reasonable. We conjecture that the reason for the success of our approach lies in the linearity of the underlying Boltzmann equation of the photon gas. The method is illustrated and discussed for grey matter and for a simple example of nongrey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.
Energy Technology Data Exchange (ETDEWEB)
Koeijer, Gelein M. de
2002-05-01
In this thesis the entropy production rates of diabatic distillation columns and a SO{sub 2} converter were minimised. This is the same as maximising the second law energy efficiency of the systems. The development of chemical industry can be made more sustainable by knowing this minimum. We found that the entropy production rate of distillation could be reduced up to 50 %. In order to achieve this reduction, heat exchangers were added on each tray. The characteristics of an optimum distillation column were presented. Furthermore, the entropy production rate of a SO{sub 2} converter was reduced with 16.7 % by altering the heights of catalytic beds, transfer areas of heat exchangers, and temperature differences over heat exchangers. These reductions show that there is still a large improvement potential in chemical industry. By applying the improved operations the world oil production can be reduced in the order of magnitude of 1 %. A similar reduction in the emission of the greenhouse gas CO{sub 2} can be expected. For deriving the entropy production rate in a systematic manner the theory of irreversible thermodynamics was useful. A simpler and a more complicated equation for the entropy production rate of distillation were derived. The simpler equation used only one force-flux product. It was suitable for minimisation of the entropy production rate of columns with the assumption of equilibrium between the outlets on each tray. The more complicated equation was able to describe satisfactorily the entropy production rate of an experimental column that separated the non-ideal mixture water-ethanol. It was next used to derive an extended set of transport equations for distillation, that includes the interface and the Soret effect (or thermal diffusion). Finally, irreversible thermodynamics was used to describe the contribution to the entropy production rate of heat transfer in heat exchangers. This contribution had a significant impact on the results of the
Extended irreversible thermodynamics and the Jeffreys type constitutive equations
International Nuclear Information System (INIS)
Serdyukov, S.I.
2003-01-01
A postulate of extended irreversible thermodynamics is considered, according to which the entropy density is a function of the internal energy, the specific volume, and their material time derivatives. On the basis of this postulate, entropy balance equations and phenomenological equations are obtained, which directly lead to the Jeffreys type constitutive equations
Entropy budget of the earth,atmosphere and ocean system
Institute of Scientific and Technical Information of China (English)
GAN Zijun; YAN Youfangand; QI Yiquan
2004-01-01
The energy budget in the system of the earth, atmosphere and ocean conforms to the first law of thermodynamics, namely the law of conservation of energy, and it is balanced when the system is in a steady-state condition. However, the entropy budget following the second law of thermodynamics is unbalanced. In this paper, we deduce the expressions of entropy flux and re-estimate the earth, atmosphere and ocean annual mean entropy budget with the updated climatologically global mean energy budget and the climatologically air-sea flux data. The calculated results show that the earth system obtains a net influx of negative entropy (-1179.3 mWm-2K-1) from its surroundings, and the atmosphere and the ocean systems obtain a net input of negative entropy at about -537.4 mWm-2K-1 and -555.6 mWm-2K-1, respectively. Calculations of the entropy budget can provide some guidance for further understanding the spatial-temporal change of the local entropy flux, and the entropy production resulting from all kinds of irreversible processes inside these systems.
Directory of Open Access Journals (Sweden)
Axel Kleidon
2010-03-01
Full Text Available The Maximum Entropy Production (MEP principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all Earth system processes are subject to the conservation of energy, mass and momentum, we argue that in practical terms the MEP principle should be applied to Earth system processes in terms of the already established framework of non-equilibrium thermodynamics, with the assumption of local thermodynamic equilibrium at the appropriate scales.
Pols, A.J.K.; Romijn, H.A.; Collste, G.; Reuter, L.
2014-01-01
In this paper we evaluate how irreversible social change should be evaluated from an ethical perspective. First; we analyse the notion of irreversibility in general terms. We define a general notion of what makes a change irreversible; drawing on discussions in ecology and economics. This notion is
The different paths to entropy
International Nuclear Information System (INIS)
Benguigui, L
2013-01-01
In order to understand how the complex concept of entropy emerged, we propose a trip into the past, reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since Gibbs's work is not very well known we present a detailed analysis, recalling the three definitions of entropy that Gibbs gives. The introduction of entropy in quantum mechanics gives in a compact form all the classical definitions of entropy. Perhaps one of the most important aspects of entropy is to see it as a thermodynamic potential like the others proposed by Callen. The calculation of fluctuations in thermodynamic quantities is thus naturally related to entropy. We close with some remarks on entropy and irreversibility. (paper)
Irreversible performance of a quantum harmonic heat engine
Rezek, Yair; Kosloff, Ronnie
2006-05-01
The unavoidable irreversible loss of power in a heat engine is found to be of quantum origin. Following thermodynamic tradition, a model quantum heat engine operating in an Otto cycle is analysed, where the working medium is composed of an ensemble of harmonic oscillators and changes in volume correspond to changes in the curvature of the potential well. Equations of motion for quantum observables are derived for the complete cycle of operation. These observables are sufficient to determine the state of the system and with it all thermodynamical variables. Once the external controls are set, the engine settles to a limit cycle. Conditions for optimal work, power and entropy production are derived. At high temperatures and quasistatic operating conditions, the efficiency at maximum power coincides with the endoreversible result \\eta_q=1-\\sqrt{{T_c}/{T_h}} . The optimal compression ratio varies from {\\cal C} =\\sqrt{T_h/T_c} in the quasistatic limit where the irreversibility is dominated by heat conductance to {\\cal C} =(T_h/T_c)^{1/4} in the sudden limit when the irreversibility is dominated by friction. When the engine deviates from adiabatic conditions, the performance is subject to friction. The origin of this friction can be traced to the noncommutability of the kinetic and potential energy of the working medium.
Brownian motion, dynamical randomness and irreversibility
International Nuclear Information System (INIS)
Gaspard, Pierre
2005-01-01
A relationship giving the entropy production as the difference between a time-reversed entropy per unit time and the standard one is applied to stochastic processes of diffusion of Brownian particles between two reservoirs at different concentrations. The entropy production in the nonequilibrium steady state is interpreted in terms of a time asymmetry in the dynamical randomness between the forward and backward paths of the diffusion process
International Nuclear Information System (INIS)
Ojima, Izumi
1989-01-01
With aid of the so-called dilation method, a concise formula is obtained for the entropy production in the algebraic formulation of quantum dynamical systems. In this framework, the initial ergodic state of an external force system plays a pivotal role in generating dissipativity as a conditional expectation. The physical meaning of van Hove limit is clarified through the scale-changing transformation to control transitions between microscopic and macroscopic levels. It plays a crucial role in realizing the macroscopic stationary in the presence of microscopic fluctuations as well as in the transition from non-Markovian (groupoid) dynamics to Markovian dissipative processes of state changes. The extension of the formalism to cases with spatial and internal inhomogeneity is indicated in the light of the groupoid dynamical systems and noncommutative integration theory
Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution.
Kleidon, Axel
2010-01-13
The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system's state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth's past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning. This journal is © 2010 The Royal Society
Tang, Qingxin; Bo, Yanchen; Zhu, Yuxin
2016-04-01
Merging multisensor aerosol optical depth (AOD) products is an effective way to produce more spatiotemporally complete and accurate AOD products. A spatiotemporal statistical data fusion framework based on a Bayesian maximum entropy (BME) method was developed for merging satellite AOD products in East Asia. The advantages of the presented merging framework are that it not only utilizes the spatiotemporal autocorrelations but also explicitly incorporates the uncertainties of the AOD products being merged. The satellite AOD products used for merging are the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 5.1 Level-2 AOD products (MOD04_L2) and the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Deep Blue Level 2 AOD products (SWDB_L2). The results show that the average completeness of the merged AOD data is 95.2%,which is significantly superior to the completeness of MOD04_L2 (22.9%) and SWDB_L2 (20.2%). By comparing the merged AOD to the Aerosol Robotic Network AOD records, the results show that the correlation coefficient (0.75), root-mean-square error (0.29), and mean bias (0.068) of the merged AOD are close to those (the correlation coefficient (0.82), root-mean-square error (0.19), and mean bias (0.059)) of the MODIS AOD. In the regions where both MODIS and SeaWiFS have valid observations, the accuracy of the merged AOD is higher than those of MODIS and SeaWiFS AODs. Even in regions where both MODIS and SeaWiFS AODs are missing, the accuracy of the merged AOD is also close to the accuracy of the regions where both MODIS and SeaWiFS have valid observations.
Quantum chaos: entropy signatures
International Nuclear Information System (INIS)
Miller, P.A.; Sarkar, S.; Zarum, R.
1998-01-01
A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)
Murashita, Yûto; Gong, Zongping; Ashida, Yuto; Ueda, Masahito
2017-10-01
The thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate the thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and postselection must be considered in the backward process, in sharp contrast to the classical case. The state reduction associated with quantum measurement, in general, creates a zero-probability region in the space of quantum trajectories of the forward process, which causes singularly strong irreversibility with divergent entropy production (i.e., absolute irreversibility) and hence makes the ordinary fluctuation theorem break down. In the classical case, the error-free measurement ordinarily leads to absolute irreversibility, because the measurement restricts classical paths to the region compatible with the measurement outcome. In contrast, in open quantum systems, absolute irreversibility is suppressed even in the presence of the projective measurement due to those quantum rare events that go through the classically forbidden region with the aid of quantum coherent driving. This suppression of absolute irreversibility exemplifies the thermodynamic advantage of quantum coherent driving. Absolute irreversibility is shown to emerge in the absence of coherent driving after the measurement, especially in systems under time-delayed feedback control. We show that absolute irreversibility is mitigated by increasing the duration of quantum coherent driving or decreasing the delay time of feedback control.
International Nuclear Information System (INIS)
Kolb, E.W.; Lindley, D.; Seckel, D.
1984-01-01
For a cosmological model with d noncompact and D compact spatial dimensions and symmetry R 1 x S/sup d/ x S/sup D/, we calculate the entropy produced in d dimensions due to the compactification of D dimensions and show it too small to be of cosmological interest. Although insufficient entropy is produced in the model we study, the contraction of extra dimensions does lead to entropy production. We discuss modifications of our assumptions, including changing our condition for decoupling of the extra dimensions, which may lead to a large entropy production and change our conclusions
Bianchi, Eugenio; De Lorenzo, Tommaso; Smerlak, Matteo
2015-06-01
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that ( i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, ( ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, ( iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.
Glavatskiy, K S
2015-10-28
Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper, we address this question by suggesting a variational formulation of irreversible evolution of a system with non-zero thermodynamic inertia. We introduce the Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" systems. We show that the standard evolution equations, in particular, the Maxwell-Cattaneo-Vernotte equation, can be derived from the variational procedure without going beyond the assumption of local equilibrium. We also argue that the second law of thermodynamics in non-equilibrium should be understood as a consequence of the variational procedure and the property of local equilibrium. For systems with instantaneous response this leads to the standard requirement of the local instantaneous entropy production being always positive. However, if a system is characterized by delayed response, the formulation of the second law of thermodynamics should be altered. In particular, the quantity, which is always positive, is not the instantaneous entropy production, but the entropy production averaged over a proper time interval.
International Nuclear Information System (INIS)
Glavatskiy, K. S.
2015-01-01
Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper, we address this question by suggesting a variational formulation of irreversible evolution of a system with non-zero thermodynamic inertia. We introduce the Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” systems. We show that the standard evolution equations, in particular, the Maxwell-Cattaneo-Vernotte equation, can be derived from the variational procedure without going beyond the assumption of local equilibrium. We also argue that the second law of thermodynamics in non-equilibrium should be understood as a consequence of the variational procedure and the property of local equilibrium. For systems with instantaneous response this leads to the standard requirement of the local instantaneous entropy production being always positive. However, if a system is characterized by delayed response, the formulation of the second law of thermodynamics should be altered. In particular, the quantity, which is always positive, is not the instantaneous entropy production, but the entropy production averaged over a proper time interval
Irreversible processes kinetic theory
Brush, Stephen G
2013-01-01
Kinetic Theory, Volume 2: Irreversible Processes deals with the kinetic theory of gases and the irreversible processes they undergo. It includes the two papers by James Clerk Maxwell and Ludwig Boltzmann in which the basic equations for transport processes in gases are formulated, together with the first derivation of Boltzmann's ""H-theorem"" and a discussion of this theorem, along with the problem of irreversibility.Comprised of 10 chapters, this volume begins with an introduction to the fundamental nature of heat and of gases, along with Boltzmann's work on the kinetic theory of gases and s
International Nuclear Information System (INIS)
Garcia-Morales, Vladimir; Pellicer, Julio; Manzanares, Jose A.
2008-01-01
We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization
DFT study of the hexagonal high-entropy alloy fission product system
Energy Technology Data Exchange (ETDEWEB)
King, D.J.M., E-mail: daniel.miks@live.com [School of Electrical Engineering, University of New South Wales, Kensington, 2052, NSW (Australia); Institute of Materials Engineering, Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW (Australia); Burr, P.A.; Obbard, E.G. [School of Electrical Engineering, University of New South Wales, Kensington, 2052, NSW (Australia); Institute of Materials Engineering, Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW (Australia); Middleburgh, S.C. [Westinghouse Electric Sweden AB, SE-721 63, Västerås (Sweden); Department of Materials, Imperial College London, South Kensington, London, SW7 2AZ (United Kingdom); KTH Royal Institute of Technology, Reactor Physics, 106 91 Stockholm (Sweden)
2017-05-15
The metallic phase fission product containing Mo-Pd-Rh-Ru-Tc can be described as a hexagonal high-entropy alloy (HEA) and is thus investigated using atomic scale simulation techniques relevant to HEAs. Contrary to previous assumptions, the removal of Tc from the system to form the Mo-Pd-Rh-Ru analog is predicted to reduce the stability of the solid solution to the point that σ-Mo{sub 5}Ru{sub 3} may precipitate out at typical fuel operating temperatures. The drive for segregation is attributed to the increased stability of the solid solution with the ejection of Mo and Ru. When Tc is included in the system, a single phase hexagonal solid solution is expected to form for a wider range of compositions. Furthermore, when cooled below 700 °C, this single phase solid solution is predicted to transition to a partially ordered structure. Future studies using the Tc-absent analogue will need to take these structural and chemical deliberations into consideration.
International Nuclear Information System (INIS)
Bianchi, Eugenio; Lorenzo, Tommaso De; Smerlak, Matteo
2015-01-01
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole “exterior entropy” and “radiation entropy.” For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the “black hole fireworks” model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that (i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, (ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the “purifying” phase, (iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.
Irreversible thermodynamic analysis and application for molecular heat engines
Lucia, Umberto; Açıkkalp, Emin
2017-09-01
Is there a link between the macroscopic approach to irreversibility and microscopic behaviour of the systems? Consumption of free energy keeps the system away from a stable equilibrium. Entropy generation results from the redistribution of energy, momentum, mass and charge. This concept represents the essence of the thermodynamic approach to irreversibility. Irreversibility is the result of the interaction between systems and their environment. The aim of this paper is to determine lost works in a molecular engine and compare results with macro (classical) heat engines. Firstly, irreversible thermodynamics are reviewed for macro and molecular cycles. Secondly, irreversible thermodynamics approaches are applied for a quantum heat engine with -1/2 spin system. Finally, lost works are determined for considered system and results show that macro and molecular heat engines obey same limitations. Moreover, a quantum thermodynamic approach is suggested in order to explain the results previously obtained from an atomic viewpoint.
Adjoint entropy vs topological entropy
Giordano Bruno, Anna
2012-01-01
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...
Bernstein, R. B.; Levine, R. D.
1972-01-01
Optimal means of characterizing the distribution of product energy states resulting from reactive collisions of molecules with restricted distributions of initial states are considered, along with those for characterizing the particular reactant state distribution which yields a given set of product states at a specified total energy. It is suggested to represent the energy-dependence of global-type results in the form of square-faced bar plots, and of data for specific-type experiments as triangular-faced prismatic plots. The essential parameters defining the internal state distribution are isolated, and the information content of such a distribution is put on a quantitative basis. The relationship between the information content, the surprisal, and the entropy of the continuous distribution is established. The concept of an entropy deficiency, which characterizes the specificity of product state formation, is suggested as a useful measure of the deviance from statistical behavior. The degradation of information by experimental averaging is considered, leading to bounds on the entropy deficiency.
Entropy production in a fluid-solid system far from thermodynamic equilibrium.
Chung, Bong Jae; Ortega, Blas; Vaidya, Ashwin
2017-11-24
The terminal orientation of a rigid body in a moving fluid is an example of a dissipative system, out of thermodynamic equilibrium and therefore a perfect testing ground for the validity of the maximum entropy production principle (MaxEP). Thus far, dynamical equations alone have been employed in studying the equilibrium states in fluid-solid interactions, but these are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive. In our past work, we have shown that the MaxEP is a reliable tool to help predict orientational equilibrium states of highly symmetric bodies such as cylinders, spheroids and toroidal bodies. The MaxEP correctly helps choose the stable equilibrium in these cases when the system is slightly out of thermodynamic equilibrium. In the current paper, we expand our analysis to examine i) bodies with fewer symmetries than previously reported, for instance, a half-ellipse and ii) when the system is far from thermodynamic equilibrium. Using two-dimensional numerical studies at Reynolds numbers ranging between 0 and 14, we examine the validity of the MaxEP. Our analysis of flow past a half-ellipse shows that overall the MaxEP is a good predictor of the equilibrium states but, in the special case of the half-ellipse with aspect ratio much greater than unity, the MaxEP is replaced by the Min-MaxEP, at higher Reynolds numbers when inertial effects come into play. Experiments in sedimentation tanks and with hinged bodies in a flow tank confirm these calculations.
Gutierrez-Jurado, H. A.; Guan, H.; Wang, J.; Wang, H.; Bras, R. L.; Simmons, C. T.
2015-12-01
Quantification of evapotranspiration (ET) and its partition over regions of heterogeneous topography and canopy poses a challenge using traditional approaches. In this study, we report the results of a novel field experiment design guided by the Maximum Entropy Production model of ET (MEP-ET), formulated for estimating evaporation and transpiration from homogeneous soil and canopy. A catchment with complex terrain and patchy vegetation in South Australia was instrumented to measure temperature, humidity and net radiation at soil and canopy surfaces. Performance of the MEP-ET model to quantify transpiration and soil evaporation was evaluated during wet and dry conditions with independently and directly measured transpiration from sapflow and soil evaporation using the Bowen Ratio Energy Balance (BREB). MEP-ET transpiration shows remarkable agreement with that obtained through sapflow measurements during wet conditions, but consistently overestimates the flux during dry periods. However, an additional term introduced to the original MEP-ET model accounting for higher stomatal regulation during dry spells, based on differences between leaf and air vapor pressure deficits and temperatures, significantly improves the model performance. On the other hand, MEP-ET soil evaporation is in good agreement with that from BREB regardless of moisture conditions. The experimental design allows a plot and tree scale quantification of evaporation and transpiration respectively. This study confirms for the first time that the MEP-ET originally developed for homogeneous open bare soil and closed canopy can be used for modeling ET over heterogeneous land surfaces. Furthermore, we show that with the addition of an empirical function simulating the plants ability to regulate transpiration, and based on the same measurements of temperature and humidity, the method can produce reliable estimates of ET during both wet and dry conditions without compromising its parsimony.
Kleidon, A.
2010-01-01
The Earth system is remarkably different from its planetary neighbours in that it shows pronounced, strong global cycling of matter. These global cycles result in the maintenance of a unique thermodynamic state of the Earth's atmosphere which is far from thermodynamic equilibrium (TE). Here, I provide a simple introduction of the thermodynamic basis to understand why Earth system processes operate so far away from TE. I use a simple toy model to illustrate the application of non-equilibrium thermodynamics and to classify applications of the proposed principle of maximum entropy production (MEP) to such processes into three different cases of contrasting flexibility in the boundary conditions. I then provide a brief overview of the different processes within the Earth system that produce entropy, review actual examples of MEP in environmental and ecological systems, and discuss the role of interactions among dissipative processes in making boundary conditions more flexible. I close with a brief summary and conclusion. PMID:20368248
Kleidon, A
2010-05-12
The Earth system is remarkably different from its planetary neighbours in that it shows pronounced, strong global cycling of matter. These global cycles result in the maintenance of a unique thermodynamic state of the Earth's atmosphere which is far from thermodynamic equilibrium (TE). Here, I provide a simple introduction of the thermodynamic basis to understand why Earth system processes operate so far away from TE. I use a simple toy model to illustrate the application of non-equilibrium thermodynamics and to classify applications of the proposed principle of maximum entropy production (MEP) to such processes into three different cases of contrasting flexibility in the boundary conditions. I then provide a brief overview of the different processes within the Earth system that produce entropy, review actual examples of MEP in environmental and ecological systems, and discuss the role of interactions among dissipative processes in making boundary conditions more flexible. I close with a brief summary and conclusion.
Entropy generation in a diesel engine turbocharging system
International Nuclear Information System (INIS)
Nakonieczny, K.
2002-01-01
The paper describes a model of entropy production in a diesel engine turbocharging system, discussing the processes occurring in the compressor, turbine, piping system, charge-air cooler and valves with the exclusion of combustion. The charging efficiency of the system is studied in two distinct engine operating states, conforming to maximum torque and nominal power conditions. Unlike in the standard approach, where the irreversibilities are derived from the balance equation for exergy and thus are addressed inexactly, the criterion function based on the notion of entropy generation, introduced in this paper, improves second law analysis of turbocharged engines by accounting for a direct description of the system internal irreversibilities. This function is used for the examination of an impact of the system design parameters on its efficiency. Computations based on the unsteady one-dimensional flow model show that, under the variations of the inlet pipe length, the timings of inlet valve opening and exhaust valve closure, and the valve overlap period, a favourable correlation can be found between the decrease of entropy production and the increase in amount of air charged into the engine cylinders. The other variables under study, including the turbine equivalent area, temperature decrease in intercooler and wastegate effective area ratio, show an opposite correlation, and thus, can be viewed as constraints in the system optimisation
Entropy Generation Across Earth's Bow Shock
Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew;
2011-01-01
Earth's bow shock is a transition layer that causes an irreversible change in the state of plasma that is stationary in time. Theories predict entropy increases across the bow shock but entropy has never been directly measured. Cluster and Double Star plasma experiments measure 3D plasma distributions upstream and downstream of the bow shock that allow calculation of Boltzmann's entropy function H and his famous H-theorem, dH/dt O. We present the first direct measurements of entropy density changes across Earth's bow shock. We will show that this entropy generation may be part of the processes that produce the non-thermal plasma distributions is consistent with a kinetic entropy flux model derived from the collisionless Boltzmann equation, giving strong support that solar wind's total entropy across the bow shock remains unchanged. As far as we know, our results are not explained by any existing shock models and should be of interests to theorists.
A parametrization of two-dimensional turbulence based on a maximum entropy production principle with a local conservation of energy
International Nuclear Information System (INIS)
Chavanis, Pierre-Henri
2014-01-01
In the context of two-dimensional (2D) turbulence, we apply the maximum entropy production principle (MEPP) by enforcing a local conservation of energy. This leads to an equation for the vorticity distribution that conserves all the Casimirs, the energy, and that increases monotonically the mixing entropy (H-theorem). Furthermore, the equation for the coarse-grained vorticity dissipates monotonically all the generalized enstrophies. These equations may provide a parametrization of 2D turbulence. They do not generally relax towards the maximum entropy state. The vorticity current vanishes for any steady state of the 2D Euler equation. Interestingly, the equation for the coarse-grained vorticity obtained from the MEPP turns out to coincide, after some algebraic manipulations, with the one obtained with the anticipated vorticity method. This shows a connection between these two approaches when the conservation of energy is treated locally. Furthermore, the newly derived equation, which incorporates a diffusion term and a drift term, has a nice physical interpretation in terms of a selective decay principle. This sheds new light on both the MEPP and the anticipated vorticity method. (paper)
The improvement of Clausius entropy and its application in entropy analysis
Institute of Scientific and Technical Information of China (English)
WU Jing; GUO ZengYuan
2008-01-01
The defects of Cleusius entropy which Include s premise of reversible process and a process quantlty of heat in Its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state funcllon. Unlike Clausius entropy, the improved deflnltion consists of system properties wlthout premise just like other state functions, for example, pressure p and enthalpy h, etc. it is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved deflnitlon of Clausius entropy provides a clear concept as well as a convenient method for en-tropy change calculation.
Entropy of measurement and erasure: Szilard's membrane model revisited
Leff, Harvey S.; Rex, Andrew F.
1994-11-01
It is widely believed that measurement is accompanied by irreversible entropy increase. This conventional wisdom is based in part on Szilard's 1929 study of entropy decrease in a thermodynamic system by intelligent intervention (i.e., a Maxwell's demon) and Brillouin's association of entropy with information. Bennett subsequently argued that information acquisition is not necessarily irreversible, but information erasure must be dissipative (Landauer's principle). Inspired by the ensuing debate, we revisit the membrane model introduced by Szilard and find that it can illustrate and clarify (1) reversible measurement, (2) information storage, (3) decoupling of the memory from the system being measured, and (4) entropy increase associated with memory erasure and resetting.
Directory of Open Access Journals (Sweden)
Lv Xiaogui
2006-11-01
Full Text Available Abstract Background There are many differences between healthy tissue and growing tumor tissue, including metabolic, structural and thermodynamic differences. Both structural and thermodynamic differences can be used to follow the entropy differences in cancerous and normal tissue. Entropy production is a bilinear form of the rates of irreversible processes and the corresponding "generalized forces". Entropy production due to various dissipation mechanisms based on temperature differences, chemical potential gradient, chemical affinity, viscous stress and exerted force is a promising tool for calculations relating to potential targets for tumor isolation and demarcation. Methods The relative importance of five forms of entropy production was assessed through mathematical estimation. Using our mathematical model we demonstrated that the rate of entropy production by a cancerous cell is always higher than that of a healthy cell apart from the case of the application of external energy. Different rates of entropy production by two kinds of cells influence the direction of entropy flow between the cells. Entropy flow from a cancerous cell to a healthy cell transfers information regarding the cancerous cell and propagates its invasive action to the healthy tissues. To change the direction of entropy flow, in addition to designing certain biochemical pathways to reduce the rate of entropy production by cancerous cells, we suggest supplying external energy to the tumor area, changing the relative rate of entropy production by the two kinds of cells and leading to a higher entropy accumulation in the surrounding normal cells than in the tumorous cells. Conclusion Through the use of mathematical models it was quantitatively demonstrated that when no external force field is applied, the rate of entropy production of cancerous cells is always higher than that of healthy cells. However, when the external energy of square wave electric pulses is applied to
Lorenz, Ralph D
2010-05-12
The 'two-box model' of planetary climate is discussed. This model has been used to demonstrate consistency of the equator-pole temperature gradient on Earth, Mars and Titan with what would be predicted from a principle of maximum entropy production (MEP). While useful for exposition and for generating first-order estimates of planetary heat transports, it has too low a resolution to investigate climate systems with strong feedbacks. A two-box MEP model agrees well with the observed day : night temperature contrast observed on the extrasolar planet HD 189733b.
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Extended Irreversible Thermodynamics
Jou, David
2010-01-01
This is the 4th edition of the highly acclaimed monograph on Extended Irreversible Thermodynamics, a theory that goes beyond the classical theory of irreversible processes. In contrast to the classical approach, the basic variables describing the system are complemented by non-equilibrium quantities. The claims made for extended thermodynamics are confirmed by the kinetic theory of gases and statistical mechanics. The book covers a wide spectrum of applications, and also contains a thorough discussion of the foundations and the scope of the current theories on non-equilibrium thermodynamics. For this new edition, the authors critically revised existing material while taking into account the most recent developments in fast moving fields such as heat transport in micro- and nanosystems or fast solidification fronts in materials sciences. Several fundamental chapters have been revisited emphasizing physics and applications over mathematical derivations. Also, fundamental questions on the definition of non-equil...
Entropy of international trades
Oh, Chang-Young; Lee, D.-S.
2017-05-01
The organization of international trades is highly complex under the collective efforts towards economic profits of participating countries given inhomogeneous resources for production. Considering the trade flux as the probability of exporting a product from a country to another, we evaluate the entropy of the world trades in the period 1950-2000. The trade entropy has increased with time, and we show that it is mainly due to the extension of trade partnership. For a given number of trade partners, the mean trade entropy is about 60% of the maximum possible entropy, independent of time, which can be regarded as a characteristic of the trade fluxes' heterogeneity and is shown to be derived from the scaling and functional behaviors of the universal trade-flux distribution. The correlation and time evolution of the individual countries' gross-domestic products and the number of trade partners show that most countries achieved their economic growth partly by extending their trade relationship.
Nonsymmetric entropy and maximum nonsymmetric entropy principle
International Nuclear Information System (INIS)
Liu Chengshi
2009-01-01
Under the frame of a statistical model, the concept of nonsymmetric entropy which generalizes the concepts of Boltzmann's entropy and Shannon's entropy, is defined. Maximum nonsymmetric entropy principle is proved. Some important distribution laws such as power law, can be derived from this principle naturally. Especially, nonsymmetric entropy is more convenient than other entropy such as Tsallis's entropy in deriving power laws.
The improvement of Clausius entropy and its application in entropy analysis
Institute of Scientific and Technical Information of China (English)
2008-01-01
The defects of Clausius entropy which include a premise of reversible process and a process quantity of heat in its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state function. Unlike Clausius entropy, the improved definition consists of system properties without premise just like other state functions, for example, pressure p and enthalpy h, etc. It is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved definition of Clausius entropy provides a clear concept as well as a convenient method for en- tropy change calculation.
International Nuclear Information System (INIS)
De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I
2007-01-01
The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation
Irreversibility of world-sheet renormalization group flow
International Nuclear Information System (INIS)
Oliynyk, T.; Suneeta, V.; Woolgar, E.
2005-01-01
We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in α ' in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target manifolds. In the case of somewhere-negative scalar curvature (of the target space), we give a proof by constructing an entropy that increases monotonically along the flow, based on Perelman's Ricci flow entropy. One consequence is the absence of periodic solutions, and we are able to give a second, direct proof of this. If the scalar curvature is everywhere positive, we instead construct a regularized volume to provide an entropy for the flow. Our results are, in a sense, the analogue of Zamolodchikov's c-theorem for world-sheet RG flows on noncompact spacetimes (though our entropy is not the Zamolodchikov C-function)
International Nuclear Information System (INIS)
Maes, Christian
2012-01-01
In contrast to the quite unique entropy concept useful for systems in (local) thermodynamic equilibrium, there is a variety of quite distinct nonequilibrium entropies, reflecting different physical points. We disentangle these entropies as they relate to heat, fluctuations, response, time asymmetry, variational principles, monotonicity, volume contraction or statistical forces. However, not all of those extensions yield state quantities as understood thermodynamically. At the end we sketch how aspects of dynamical activity can take over for obtaining an extended Clausius relation.
Ecological optimization and parametric study of irreversible Stirling and Ericsson heat pumps
International Nuclear Information System (INIS)
Tyagi, S.K.; Kaushik, S.C.; Salohtra, R.
2002-01-01
This communication presents the ecological optimization and parametric study of irreversible Stirling and Ericsson heat pump cycles, in which the external irreversibility is due to finite temperature difference between working fluid and external reservoirs while the internal irreversibilities are due to regenerative heat loss and other entropy generations within the cycle. The ecological function is defined as the heating load minus the irreversibility (power loss) which is ambient temperature times the entropy generation. The ecological function is optimized with respect to working fluid temperatures, and the expressions for various parameters at the optimal operating condition are obtained. The effects of different operating parameters on the performance of these cycles have been studied. It is found that the effect of internal irreversibility parameter is more pronounced than the other parameters on the performance of these cycles. (author)
Machine Selection in A Dairy Product Company with Entropy and SAW Method Integration
Directory of Open Access Journals (Sweden)
Aşkın Özdağoğlu
2017-07-01
Full Text Available Machine selection is an important and difficult process for the firms, and its results may generate more problems than anticipated. In order to find the best alternative, managers should define the requirements of the factory and determine the necessary criteria. On the other hand, the decision making criteria in order to choose the right equipment may vary according to the type of the manufacturing facility, market requirements, and consumer assigned criteria. This study aims to find the best machine alternative among the three machine offerings according to twelve evaluation criteria by integrating entropy method with SAW method.
International Nuclear Information System (INIS)
Ye, Xuemin; Li, Chunxi
2013-01-01
As one of the most significant measures to improve energy utilization efficiency and save energy, cogeneration or combined heat and power (CHP) has been widely applied and promoted with positive motivations in many countries. A rational cost allocation model should indicate the performance of cogenerations and balance the benefits between electricity generation and heat production. Based on the second law of thermodynamics, the present paper proposes an entropy change method for cost allocation by choosing exhaust steam entropy as a datum point, and the new model works in conjunction with entropy change and irreversibility during energy conversion processes. The allocation ratios of heat cost with the present and existing methods are compared for different types of cogenerations. Results show that the allocation ratios with the entropy change method are more rational and the cost allocation model can make up some limitations involved in other approaches. The future energy policies and innovational directions for cogenerations and heat consumers should be developed. - Highlights: • A rational model of cogeneration cost allocation is established. • Entropy change method integrates the relation of entropy change and exergy losses. • The unity of measuring energy quality and quantity is materialized. • The benefits between electricity generation and heat production are balanced
Mass-independent area (or entropy) and thermodynamic volume products in conformal gravity
Pradhan, Parthapratim
2017-06-01
In this work, we investigate the thermodynamic properties of conformal gravity in four dimensions. We compute the area (or entropy) functional relation for this black hole (BH). We consider both de Sitter (dS) and anti-de Sitter (AdS) cases. We derive the Cosmic-Censorship-Inequality which is an important relation in general relativity that relates the total mass of a spacetime to the area of all the BH horizons. Local thermodynamic stability is studied by computing the specific heat. The second-order phase transition occurs at a certain condition. Various types of second-order phase structure have been given for various values of a and the cosmological constant Λ in the Appendix. When a = 0, one obtains the result of Schwarzschild-dS and Schwarzschild-AdS cases. In the limit aM ≪ 1, one obtains the result of Grumiller spacetime, where a is nontrivial Rindler parameter or Rindler acceleration and M is the mass parameter. The thermodynamic volume functional relation is derived in the extended phase space, where the cosmological constant is treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. The mass-independent area (or entropy) functional relation and thermodynamic volume functional relation that we have derived could turn out to be a universal quantity.
Matthaeus, W. H.; Yang, Y.; Servidio, S.; Parashar, T.; Chasapis, A.; Roytershteyn, V.
2017-12-01
Turbulence cascade transfers energy from large scale to small scale but what happens once kinetic scales are reached? In a collisional medium, viscosity and resistivity remove fluctuation energy in favor of heat. In the weakly collisional solar wind, (or corona, m-sheath, etc.), the sequence of events must be different. Heating occurs, but through what mechanisms? In standard approaches, dissipation occurs though linear wave modes or instabilities and one seeks to identify them. A complementary view is that cascade leads to several channels of energy conversion, interchange and spatial rearrangement that collectively leads to production of internal energy. Channels may be described using compressible MHD & multispecies Vlasov Maxwell formulations. Key steps are: Conservative rearrangement of energy in space; Parallel incompressible and compressible cascades - conservative rearrangment in scale; electromagnetic work on particles that drives flows, both macroscopic and microscopic; and pressure-stress interactions, both compressive and shear-like, that produces internal energy. Examples given from MHD, PIC simulations and MMS observations. A more subtle issue is how entropy is related to this degeneration (or, "dissipation") of macroscopic, fluid-scale fluctuations. We discuss this in terms of Boltzmann and thermodynamic entropies, and velocity space effects of collisions.
Directory of Open Access Journals (Sweden)
Donghai Wang
2011-01-01
Full Text Available The concept of entropy and its relevant principles, mainly the principle of maximum entropy production (MEP, the effect of negative entropy flow (NEF on the organization of atmospheric systems and the principle of the Second Law of thermodynamics, as well as their applications to atmospheric sciences, are reviewed. Some formulations of sub-grid processes such as diffusion parameterization schemes in computational geophysical fluid dynamics that can be improved based on full-irreversibility are also discussed, although they have not yet been systematically subjected to scrutiny from the perspective of the entropy budgets. A comparative investigation shows that the principle of MEP applies to the entropy production of macroscopic fluxes and determines the most probable state, that is, a system may choose a development meta-stable trajectory with a smaller production since entropy production behavior involves many specific dynamical and thermodynamic processes in the atmosphere and the extremal principles only provide a general insight into the overall configuration of the atmosphere. In contrast to the principle of MEP, the analysis of NEF is able to provide a new insight into the mechanism responsible for the evolution of a weather system as well as a new approach to predicting its track and intensity trend.
Nonequilibrium and irreversibility
Gallavotti, Giovanni
2014-01-01
This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of ) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending t...
A Graphical Proof of the Positive Entropy Change in Heat Transfer between Two Objects
Kiatgamolchai, Somchai
2015-01-01
It is well known that heat transfer between two objects results in a positive change in the total entropy of the two-object system. The second law of thermodynamics states that the entropy change of a naturally irreversible process is positive. In other words, if the entropy change of any process is positive, it can be inferred that such a process…
A Modified Entropy Generation Number for Heat Exchangers
Institute of Scientific and Technical Information of China (English)
无
1996-01-01
This paper demonstrates the difference between the entropy generation number method proposed by Bejian and the method of entropy generation per unit amount of heat transferred in analyzing the ther-modynamic performance of heat exchangers,points out the reason for leading to the above difference.A modified entropy generation number for evaluating the irreversibility of heat exchangers is proposed which is in consistent with the entropy generation per unit amount of heat transferred in entropy generation analysis.The entropy generated by friction is also investigated.Results show that when the entropy generated by friction in heat exchangers in taken into account,there is a minimum total entropy generation number while the NTU and the ratio of heat capacity rates vary.The existence of this minimum is the prerequisite of heat exchanger optimization.
Entropy generation in cosmological particle creation
International Nuclear Information System (INIS)
Castagnino, M.A.; Gaioli, F.H.; Sforza, D.M.
1996-01-01
A very simplified model of the Universe is considered in order to propose an alternative approach to the irreversible evolution of the Universe at very early times. The entropy generation at the quantum stage can be thought of as a consequence of an instability of the system. Then particle creation arises from this instability
Entropy and Its Correlations with Other Related Quantities
Directory of Open Access Journals (Sweden)
Jing Wu
2014-02-01
Full Text Available In order to find more correlations between entropy and other related quantities, an analogical analysis is conducted between thermal science and other branches of physics. Potential energy in various forms is the product of a conserved extensive quantity (for example, mass or electric charge and an intensive quantity which is its potential (for example, gravitational potential or electrical voltage, while energy in specific form is a dissipative quantity during irreversible transfer process (for example mechanical or electrical energy will be dissipated as thermal energy. However, it has been shown that heat or thermal energy, like mass or electric charge, is conserved during heat transfer processes. When a heat transfer process is for object heating or cooling, the potential of internal energy U is the temperature T and its potential “energy” is UT/2 (called entransy and it is the simplified expression of thermomass potential energy; when a heat transfer process is for heat-work conversion, the potential of internal energy U is (1 − T0/T, and the available potential energy of a system in reversible heat interaction with the environment is U − U0 − T0(S − S0, then T0/T and T0(S − S0 are the unavailable potential and the unavailable potential energy of a system respectively. Hence, entropy is related to the unavailable potential energy per unit environmental temperature for heat-work conversion during reversible heat interaction between the system and its environment. Entropy transfer, like other forms of potential energy transfer, is the product of the heat and its potential, the reciprocal of temperature, although it is in form of the quotient of the heat and the temperature. Thus, the physical essence of entropy transfer is the unavailable potential energy transfer per unit environmental temperature. Entropy is a non-conserved, extensive, state quantity of a system, and entropy generation in an irreversible heat transfer process
Indian Academy of Sciences (India)
Abstract. It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf f that satisfy. ∫ fhi dμ = λi for i = 1, 2,...,...k the maximizer of entropy is an f0 that is pro- portional to exp(. ∑ ci hi ) for some choice of ci . An extension of this to a continuum of.
Indian Academy of Sciences (India)
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy ∫ f h i d = i for i = 1 , 2 , … , … k the maximizer of entropy is an f 0 that is proportional to exp ( ∑ c i h i ) for some choice of c i . An extension of this to a continuum of ...
Directory of Open Access Journals (Sweden)
Tommaso Toffoli
2016-06-01
Full Text Available Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1 the system’s internal dynamics; (2 unsolicited external influences on it; and (3 the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems!
Exergetic efficiency optimization for an irreversible heat pump ...
Indian Academy of Sciences (India)
side ... For irreversible cycle, the internal irreversibility, i.e., non-isentropic losses in the ... constant thermal capacitance rate (the product of mass flow rate and specific heat), .... reversed Brayton cycle is dependent on the external heat transfer ...
Directory of Open Access Journals (Sweden)
José Ernesto Nájera-Carpio
2015-07-01
Full Text Available In this work, the irreversible processes in light heating of Silicon (Si and Germanium (Ge thin films are examined. Each film is exposed to light irradiation with radiative and convective boundary conditions. Heat, electron and hole transport and generation-recombination processes of electron-hole pairs are studied in terms of a phenomenological model obtained from basic principles of irreversible thermodynamics. We present an analysis of the contributions to the entropy production in the stationary state due to the dissipative effects associated with electron and hole transport, generation-recombination of electron-hole pairs as well as heat transport. The most significant contribution to the entropy production comes from the interaction of light with the medium in both Si and Ge. This interaction includes two processes, namely, the generation of electron-hole pairs and the transferring of energy from the absorbed light to the lattice. In Si the following contribution in magnitude comes from the heat transport. In Ge all the remaining contributions to entropy production have nearly the same order of magnitude. The results are compared and explained addressing the differences in the magnitude of the thermodynamic forces, Onsager’s coefficients and transport properties of Si and Ge.
International Nuclear Information System (INIS)
Makinde, O.D.
2005-10-01
In this paper, the first and second law of thermodynamics are employed in order to study the inherent irreversibility for a gravity driven non-Newtonian Ostwald-de Waele power law liquid film along an inclined isothermal plate. Based on some simplified assumptions, the governing equations are obtained and solved analytically. Expressions for fluid velocity, temperature, volumetric entropy generation numbers, irreversibility distribution ratio and the Bejan number are also determined. (author)
Entropy dynamics in cone production of longleaf pine forests in the southeastern United States
Xiongwen Chen; Dale G. Brockway; Qinfeng Guo
2016-01-01
Sporadic temporal patterns of seed production are a challenge for the regeneration and restoration of longleaf pine, which is a keystone component of an endangered ecosystem in the southeastern United States. In this study, long-term data for longleaf pine cone production, collected at six sites across the southeastern region, was examined from the perspective of...
Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains
Kaiser, Marcus; Jack, Robert L.; Zimmer, Johannes
2018-03-01
We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.
International Nuclear Information System (INIS)
Hudetz, T.
1989-01-01
As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)
Maximum entropy tokamak configurations
International Nuclear Information System (INIS)
Minardi, E.
1989-01-01
The new entropy concept for the collective magnetic equilibria is applied to the description of the states of a tokamak subject to ohmic and auxiliary heating. The condition for the existence of steady state plasma states with vanishing entropy production implies, on one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current. These restrictions are consistent with Goldston scaling and with the existence of a heat pinch. (author)
Shannon versus Kullback-Leibler entropies in nonequilibrium random motion
International Nuclear Information System (INIS)
Garbaczewski, Piotr
2005-01-01
We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional Kullback-Leibler entropy. Both entropies discriminate among various probability distributions, either statically or in the time domain. An asymptotic approach towards equilibrium is typically monotonic in terms of the Kullback entropy. The Shannon entropy time rate needs not to be positive and is a sensitive indicator of the power transfer processes (removal/supply) due to an active environment. In the case of Smoluchowski diffusions, the Kullback entropy time rate coincides with the Shannon entropy 'production' rate
Irreversible work in a thermal medium with colored noise
Ohkuma, Takahiro
2009-10-01
Irreversible work and its fluctuations in a classical system governed by non-Markovian stochastic dynamics are investigated. The production of irreversible work depends not only on the protocol of an operation but also on the details of the non-Markovian memory. We consider a generalized Langevin equation with a memory kernel and derive an expression for the irreversible work in the case of slow operations by carrying out an expansion of this memory kernel in the parameter representing the length of the memory. We apply our formulation to a harmonically trapped system and demonstrate the efficiency of a cycle by evaluating the irreversible work. It is found that a decrease in the irreversible work due to the memory effect can occur for an operation through which the trap is squeezed. The results for this harmonic system are verified exactly in the case that the memory kernel has exponential decay.
Irreversible work in a thermal medium with colored noise
International Nuclear Information System (INIS)
Ohkuma, Takahiro
2009-01-01
Irreversible work and its fluctuations in a classical system governed by non-Markovian stochastic dynamics are investigated. The production of irreversible work depends not only on the protocol of an operation but also on the details of the non-Markovian memory. We consider a generalized Langevin equation with a memory kernel and derive an expression for the irreversible work in the case of slow operations by carrying out an expansion of this memory kernel in the parameter representing the length of the memory. We apply our formulation to a harmonically trapped system and demonstrate the efficiency of a cycle by evaluating the irreversible work. It is found that a decrease in the irreversible work due to the memory effect can occur for an operation through which the trap is squeezed. The results for this harmonic system are verified exactly in the case that the memory kernel has exponential decay
Upper entropy axioms and lower entropy axioms
International Nuclear Information System (INIS)
Guo, Jin-Li; Suo, Qi
2015-01-01
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics
International Nuclear Information System (INIS)
Kawazura, Y.; Yoshida, Z.
2012-01-01
Two different types of self-organizing and sustaining ordered motion in fluids or plasmas--one is a Benard convection (or streamer) and the other is a zonal flow--have been compared by introducing a thermodynamic phenomenological model and evaluating the corresponding entropy production rates (EP). These two systems have different topologies in their equivalent circuits: the Benard convection is modeled by parallel connection of linear and nonlinear conductances, while the zonal flow is modeled by series connection. The ''power supply'' that drives the systems is also a determinant of operating modes. When the energy flux is a control parameter (as in usual plasma experiments), the driver is modeled by a constant-current power supply, and when the temperature difference between two separate boundaries is controlled (as in usual computational studies), the driver is modeled by a constant-voltage power supply. The parallel (series)-connection system tends to minimize (maximize) the total EP when a constant-current power supply drives the system. This minimum/maximum relation flips when a constant-voltage power supply is connected.
Analyzing the complexity of cone production in longleaf pine by multiscale entropy
Xiongwen Chen; Qinfeng Guo; Dale G. Brockway
2016-01-01
The longleaf pine (Pinus palustris Mill.) forests are important ecosystems in the southeastern USA because of their ecological and economic value. Since European settlement, longleaf pine ecosystems have dramatically declined in extent, to the degree that they are now listed as endangered ecosystems. Its sporadic seed production, which...
International Nuclear Information System (INIS)
Balkan, F.
2005-01-01
A more realistic application of the entropy minimization principle EoEP is presented. This principle dictates uniform local entropy generations along the heat exchanger in order to minimize the total entropy generation rate due only to heat transfer. For a certain heat duty and area of an existing exchanger, this is done by changing the temperatures of one fluid while the temperatures of the other fluid are held constant. Since the heat duty is fixed, the change in the temperatures of the fluid after the change, however, may sometimes cause a drastic change in its flow rate. This may cause considerable changes in the overall heat transfer coefficient (U) and, consequently, in the entropy generation rate. Depending on the choice of the fluid for changing, the new entropy generation rates may be higher or lower than those based on constant U as is the case in papers recently published. So, the classical application of the EoEP principle needs to be modified to achieve more realistic entropy generation rates. In this study, the principle of EoEP with variable U is applied to some cases of heat exchange, and a simple method is presented as a criterion for the proper choice of the fluid to be changed
Misuse of thermodynamic entropy in economics
International Nuclear Information System (INIS)
Kovalev, Andrey V.
2016-01-01
The direct relationship between thermodynamic entropy and economic scarcity is only valid for a thermodynamically isolated economy. References to the second law of thermodynamics in economics within the context of scarcity ignore the fact that the earth is not an isolated system. The earth interacts with external sources and sinks of entropy and the resulting total entropy fluctuates around a constant. Even if the mankind finally proves unable to recycle industrial waste and close the technological cycle, the economic disruption caused by the depletion of natural resources may happen while the total thermodynamic entropy of the ecosystem remains essentially at the present level, because the transfer of chemically refined products may not increase significantly the total entropy, but it may decrease their recyclability. The inutility of industrial waste is not connected with its entropy, which may be exemplified with the case of alumina production. The case also demonstrates that industrially generated entropy is discharged into surroundings without being accumulated in ‘thermodynamically unavailable matter’. Material entropy, as a measure of complexity and economic dispersal of resources, can be a recyclability metric, but it is not a thermodynamic parameter, and its growth is not equivalent to the growth of thermodynamic entropy. - Highlights: • Entropy cannot be used as a measure of economic scarcity. • There is no anthropogenic entropy separate from the entropy produced naturally. • Inutility of industrial waste is not connected with its thermodynamic entropy. • Industrially generated entropy may or may not be accumulated in industrial waste. • Recyclability is more important than thermodynamic entropy of a product.
CSIR Research Space (South Africa)
Baloyi, J
2016-07-01
Full Text Available . The irreversibilities generated were arrived at by computing the entropy generation rates due to the combustion and frictional pressure drop processes. For the combustor where the wall condition was changed from adiabatic to negative heat flux (that is heat leaving...
Ecological optimization for an irreversible magnetic Ericsson refrigeration cycle
International Nuclear Information System (INIS)
Wang Hao; Wu Guo-Xing
2013-01-01
An irreversible Ericsson refrigeration cycle model is established, in which multi-irreversibilities such as finite-rate heat transfer, regenerative loss, heat leakage, and the efficiency of the regenerator are taken into account. Expressions for several important performance parameters, such as the cooling rate, coefficient of performance (COP), power input, exergy output rate, entropy generation rate, and ecological function are derived. The influences of the heat leakage and the time of the regenerative processes on the ecological performance of the refrigerator are analyzed. The optimal regions of the ecological function, cooling rate, and COP are determined and evaluated. Furthermore, some important parameter relations of the refrigerator are revealed and discussed in detail. The results obtained here have general significance and will be helpful in gaining a deep understanding of the magnetic Ericsson refrigeration cycle. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
On unified-entropy characterization of quantum channels
International Nuclear Information System (INIS)
Rastegin, A E
2012-01-01
We consider properties of quantum channels with the use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map (q, s)-entropy is naturally defined as the unified (q, s)-entropy of a rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For the tensor product of a pair of quantum channels, we derive a two-sided estimate on the output entropy of a maximally entangled input state. (paper)
Entropy Generation Analysis of Desalination Technologies
Directory of Open Access Journals (Sweden)
John H. Lienhard V
2011-09-01
Full Text Available Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies. Entropy generation analysis, and specifically, Second Law efficiency, is an important tool for illustrating the influence of irreversibilities within a system on the required energy input. When defining Second Law efficiency, the useful exergy output of the system must be properly defined. For desalination systems, this is the minimum least work of separation required to extract a unit of water from a feed stream of a given salinity. In order to evaluate the Second Law efficiency, entropy generation mechanisms present in a wide range of desalination processes are analyzed. In particular, entropy generated in the run down to equilibrium of discharge streams must be considered. Physical models are applied to estimate the magnitude of entropy generation by component and individual processes. These formulations are applied to calculate the total entropy generation in several desalination systems including multiple effect distillation, multistage flash, membrane distillation, mechanical vapor compression, reverse osmosis, and humidification-dehumidification. Within each technology, the relative importance of each source of entropy generation is discussed in order to determine which should be the target of entropy generation minimization. As given here, the correct application of Second Law efficiency shows which systems operate closest to the reversible limit and helps to indicate which systems have the greatest potential for improvement.
Extended irreversible thermodynamics and non-equilibrium temperature
Directory of Open Access Journals (Sweden)
Casas-Vazquez, Jose'
2008-02-01
Full Text Available We briefly review the concept of non-equilibrium temperature from the perspectives of extended irreversible thermodynamics, fluctuation theory, and statistical mechanics. The relations between different proposals are explicitly examined in two especially simple systems: an ideal gas in steady shear flow and a forced harmonic oscillator in a thermal bath. We examine with special detail temperatures related to the average molecular kinetic energy along different spatial directions, to the average configurational energy, to the derivative of the entropy with respect to internal energy, to fluctuation-dissipation relation and discuss their measurement.
Prediction of Chiller Power Consumption: An Entropy Generation Approach
Saththasivam, Jayaprakash
2016-06-21
Irreversibilities in each component of vapor compression chillers contribute to additional power consumption in chillers. In this study, chiller power consumption was predicted by computing the Carnot reversible work and entropy generated in every component of the chiller. Thermodynamic properties namely enthalpy and entropy of the entire refrigerant cycle were obtained by measuring the pressure and temperature at the inlet and outlet of each primary component of a 15kW R22 water cooled scroll chiller. Entropy generation of each component was then calculated using the First and Second Laws of Thermodynamics. Good correlation was found between the measured and computed chiller power consumption. This irreversibility analysis can be also effectively used as a performance monitoring tool in vapor compression chillers as higher entropy generation is anticipated during faulty operations.
Irreversible properties of YBCO coated conductors
International Nuclear Information System (INIS)
Vostner, A.
2001-02-01
Over the past few years substantial efforts were made to optimize the fabrication techniques of various high temperature superconductors for commercial applications. In addition to Bi-2223 tapes, Y-123 coated conductors have the potential for large-scale production and are considered as the second generation of superconducting 'wires' for high current applications. This work reports on magnetic and transport current investigations of Y-123 thick films deposited on either single crystalline substrates by liquid phase epitaxy (LPE) or on metallic substrates by pulsed laser deposition (PLD). At the beginning, a short introduction of the general idea of a coated conductor and of the different production techniques is presented, followed by a description of the different experimental set-ups and the evaluation methods. The main part starts with the results obtained from SQUID magnetometry and ac-susceptibility measurements including the transition temperatures T c , the field dependence of the magnetic critical current densities and the irreversibility lines. In addition, some issues concerning the granular structure and the inter- and intragranular current distribution of the superconducting films are discussed. The investigations by transport currents are focused on the behavior of the application relevant irreversible parameters. These are the angular and the field dependence of the critical transport current densities at 77 and 60 K, as well as the temperature dependence of the irreversibility fields up to 6 T. To gain more insight into the defect structure of the films, neutron irradiation studies were performed on some samples. The introduction of these artificial pinning centers causes large enhancements of the magnetic J c in LPE specimens for the field parallel to the c-axis (H//c) at higher temperatures and magnetic fields. The granular structure of the samples does not change up to the highest neutron fluences. However, the enhancements of the transport J c
Entropy Filtered Density Function for Large Eddy Simulation of Turbulent Reacting Flows
Safari, Mehdi
Analysis of local entropy generation is an effective means to optimize the performance of energy and combustion systems by minimizing the irreversibilities in transport processes. Large eddy simulation (LES) is employed to describe entropy transport and generation in turbulent reacting flows. The entropy transport equation in LES contains several unclosed terms. These are the subgrid scale (SGS) entropy flux and entropy generation caused by irreversible processes: heat conduction, mass diffusion, chemical reaction and viscous dissipation. The SGS effects are taken into account using a novel methodology based on the filtered density function (FDF). This methodology, entitled entropy FDF (En-FDF), is developed and utilized in the form of joint entropy-velocity-scalar-turbulent frequency FDF and the marginal scalar-entropy FDF, both of which contain the chemical reaction effects in a closed form. The former constitutes the most comprehensive form of the En-FDF and provides closure for all the unclosed filtered moments. This methodology is applied for LES of a turbulent shear layer involving transport of passive scalars. Predictions show favor- able agreements with the data generated by direct numerical simulation (DNS) of the same layer. The marginal En-FDF accounts for entropy generation effects as well as scalar and entropy statistics. This methodology is applied to a turbulent nonpremixed jet flame (Sandia Flame D) and predictions are validated against experimental data. In both flows, sources of irreversibility are predicted and analyzed.
Excess Entropy and Diffusivity
Indian Academy of Sciences (India)
First page Back Continue Last page Graphics. Excess Entropy and Diffusivity. Excess entropy scaling of diffusivity (Rosenfeld,1977). Analogous relationships also exist for viscosity and thermal conductivity.
Explaining the entropy concept and entropy components
Directory of Open Access Journals (Sweden)
Marko Popovic
2018-04-01
Full Text Available Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy STM as a function of temperature T and heat capacity at constant pressure Cp: STM = ∫(Cp/T dT. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state. It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy S0 as a function of the number of molecules N and the number of distinct orientations available to them in a crystal m: S0 = N kB ln m, where kB is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system S: S = S0 + STM. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.
Thermodynamics of irreversible electrochemical phenomena
Groot, S.R. de; Mazur, P.; Tolhoek, H.A.
1953-01-01
A discussion from first principles is given of the energy and entropy laws in electrochemical systems. It is found that it is possible to clarify such controversial concepts as the form of the second law and the role of the electrochemical potential in the systems concerned.
Ecological optimization of an irreversible quantum Carnot heat engine with spin-1/2 systems
International Nuclear Information System (INIS)
Liu Xiaowei; Chen Lingen; Wu Feng; Sun Fengrui
2010-01-01
A model of a quantum heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting spin-1/2 systems is established in this paper. The quantum heat engine cycle is composed of two isothermal processes and two irreversible adiabatic processes and is referred to as a spin quantum Carnot heat engine. Based on the quantum master equation and the semi-group approach, equations of some important performance parameters, such as power output, efficiency, entropy generation rate and ecological function (a criterion representing the optimal compromise between exergy output rate and exergy loss rate), for the irreversible spin quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. The effects of internal irreversibility and heat leakage on ecological performance are discussed in detail.
Second Law Analysis of the Optimal Fin by Minimum Entropy Generation
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Based on the entropy generation concept of thermodynamics, this paper established a general theoretical model for the analysis of entropy generation to optimize fms, in which the minimum entropy generation was selected as the object to be studied. The irreversibility due to heat transfer and friction was taken into account so that the minimum entropygeneration number has been analyzed with respect to second law of thermodynamics in the forced cross-flow. The optimum dimensions of cylinder pins were discussed. It's found that the minimum entropy generation number depends on parameters related to the fluid and fin physical parameters. Variations of the minimum entropy generation number with different parameters were analyzed.
Entropy Exchange in Coupled Field-Superconducting Charge Qubit System with Intrinsic Decoherence
Institute of Scientific and Technical Information of China (English)
SHAO Bin; ZHANG Jian; ZOU Jian
2006-01-01
Based on the intrinsic decoherence effect, partial entropy properties of a super conducting charge qubitinside a single-mode cavity field is investigated, and entropy exchange which is recently regarded as a kind of anti-correlated behavior of the entropy between subsystems is explored. Our results show that although the intrinsic decoherenceleads to an effective irreversible evolution of the interacting system due to a suppression of coherent quantum features through the decay of off-diagonal matrix elements of the density operator and has an apparently influence on the partial entropy of two individual subsystems, it does not effect the entropy exchange between the two subsystems.
Directory of Open Access Journals (Sweden)
Prasad Radha K.
2017-09-01
Full Text Available This paper presents mathematical modelling and numerical analysis to evaluate entropy generation analysis (EGA by considering pressure drop and second law efficiency based on thermodynamics for forced convection heat transfer in rectangular duct of a solar air heater with wire as artificial roughness in the form of arc shape geometry on the absorber plate. The investigation includes evaluations of entropy generation, entropy generation number, Bejan number and irreversibilities of roughened as well as smooth absorber plate solar air heaters to compare the relative performances. Furthermore, effects of various roughness parameters and operating parameters on entropy generation have also been investigated. Entropy generation and irreversibilities (exergy destroyed has its minimum value at relative roughness height of 0.0422 and relative angle of attack of 0.33, which leads to the maximum exergetic efficiency. Entropy generation and exergy based analyses can be adopted for the evaluation of the overall performance of solar air heaters.
International Nuclear Information System (INIS)
Chen, Yong; Ge, Hao; Xiong, Jie; Xu, Lihu
2016-01-01
Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loève expansion of complex-valued Ornstein-Uhlenbeck process.
Intrinsic irreversibility in quantum theory
International Nuclear Information System (INIS)
Prigogine, I.; Petrosky, T.Y.
1987-01-01
Quantum theory has a dual structure: while solutions of the Schroedinger equation evolve in a deterministic and time reversible way, measurement introduces irreversibility and stochasticity. This presents a contrast to Bohr-Sommerfeld-Einstein theory, in which transitions between quantum states are associated with spontaneous and induced transitions, defined in terms of stochastic processes. A new form of quantum theory is presented here, which contains an intrinsic form of irreversibility, independent of observation. This new form applies to situations corresponding to a continuous spectrum and to quantum states with finite life time. The usual non-commutative algebra associated to quantum theory is replaced by more general algebra, in which operators are also non-distributive. Our approach leads to a number of predictions, which hopefully may be verified or refuted in the next years. (orig.)
Irreversible stochastic processes on lattices
International Nuclear Information System (INIS)
Nord, R.S.
1986-01-01
Models for irreversible random or cooperative filling of lattices are required to describe many processes in chemistry and physics. Since the filling is assumed to be irreversible, even the stationary, saturation state is not in equilibrium. The kinetics and statistics of these processes are described by recasting the master equations in infinite hierarchical form. Solutions can be obtained by implementing various techniques: refinements in these solution techniques are presented. Programs considered include random dimer, trimer, and tetramer filling of 2D lattices, random dimer filling of a cubic lattice, competitive filling of two or more species, and the effect of a random distribution of inactive sites on the filling. Also considered is monomer filling of a linear lattice with nearest neighbor cooperative effects and solve for the exact cluster-size distribution for cluster sizes up to the asymptotic regime. Additionally, a technique is developed to directly determine the asymptotic properties of the cluster size distribution. Finally cluster growth is considered via irreversible aggregation involving random walkers. In particular, explicit results are provided for the large-lattice-size asymptotic behavior of trapping probabilities and average walk lengths for a single walker on a lattice with multiple traps. Procedures for exact calculation of these quantities on finite lattices are also developed
Entropy of the system formed in heavy ion collision
International Nuclear Information System (INIS)
Gudima, K.K.; Schulz, H.; Toneev, V.D.
1985-01-01
In frames of a cascade model the entropy evolution in a system producted in heavy ion collisions is investigated. Entropy calculation is based on smoothing of the distribution function over the momentum space by the temperature field introduction. The resulting entropy per one nucleon is shown to be rather sensitive to phase space subdivision into cells at the stage of free scattering of reaction products. Compared to recent experimental results for specific entropy values inferred from the composite particle yield of 4π measurements, it is found that cascade calculations do not favour some particular entropy model treatments and suggest smaller entropy values than following from consideration within equilibrium statistics
Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf
2017-09-01
There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.
SpatEntropy: Spatial Entropy Measures in R
Altieri, Linda; Cocchi, Daniela; Roli, Giulia
2018-01-01
This article illustrates how to measure the heterogeneity of spatial data presenting a finite number of categories via computation of spatial entropy. The R package SpatEntropy contains functions for the computation of entropy and spatial entropy measures. The extension to spatial entropy measures is a unique feature of SpatEntropy. In addition to the traditional version of Shannon's entropy, the package includes Batty's spatial entropy, O'Neill's entropy, Li and Reynolds' contagion index, Ka...
Applicability of the minimum entropy generation method for optimizing thermodynamic cycles
Institute of Scientific and Technical Information of China (English)
Cheng Xue-Tao; Liang Xin-Gang
2013-01-01
Entropy generation is often used as a figure of merit in thermodynamic cycle optimizations.In this paper,it is shown that the applicability of the minimum entropy generation method to optimizing output power is conditional.The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power when the total heat into the system of interest is not prescribed.For the cycles whose working medium is heated or cooled by streams with prescribed inlet temperatures and prescribed heat capacity flow rates,it is theoretically proved that both the minimum entropy generation rate and the minimum entropy generation number correspond to the maximum output power when the virtual entropy generation induced by dumping the used streams into the environment is considered.However,the minimum principle of entropy generation is not tenable in the case that the virtual entropy generation is not included,because the total heat into the system of interest is not fixed.An irreversible Carnot cycle and an irreversible Brayton cycle are analysed.The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power if the heat into the system of interest is not prescribed.
Applicability of the minimum entropy generation method for optimizing thermodynamic cycles
International Nuclear Information System (INIS)
Cheng Xue-Tao; Liang Xin-Gang
2013-01-01
Entropy generation is often used as a figure of merit in thermodynamic cycle optimizations. In this paper, it is shown that the applicability of the minimum entropy generation method to optimizing output power is conditional. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power when the total heat into the system of interest is not prescribed. For the cycles whose working medium is heated or cooled by streams with prescribed inlet temperatures and prescribed heat capacity flow rates, it is theoretically proved that both the minimum entropy generation rate and the minimum entropy generation number correspond to the maximum output power when the virtual entropy generation induced by dumping the used streams into the environment is considered. However, the minimum principle of entropy generation is not tenable in the case that the virtual entropy generation is not included, because the total heat into the system of interest is not fixed. An irreversible Carnot cycle and an irreversible Brayton cycle are analysed. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power if the heat into the system of interest is not prescribed. (general)
Dewar, R
2003-01-01
Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First, it is shown that the probability distribution p subGAMMA of the underlying microscopic phase space trajectories GAMMA over a time interval of length tau satisfies p subGAMMA propor to exp(tau sigma subGAMMA/2k sub B) where sigma subGAMMA is the time-averaged rate of entropy production of GAMMA. Three consequences of this result are then derived: (1) the fluctuation theorem, which describes the exponentially declining probability of deviations from the second law of thermodynamics as tau -> infinity; (2) the selection principle of maximum entropy production for non-equilibrium stationary states, empirical support for which has been found in studies of phenomena as diverse as the Earth's climate and crystal growth morphology; and (3) the emergence of self-organized criticality for flux-driven systems in the slowly-driven limit. The explanation of these results on general inf...
Tran, Hai L; Lexa, Katrina W; Julien, Olivier; Young, Travis S; Walsh, Christopher T; Jacobson, Matthew P; Wells, James A
2017-02-22
Macrocycles are appealing drug candidates due to their high affinity, specificity, and favorable pharmacological properties. In this study, we explored the effects of chemical modifications to a natural product macrocycle upon its activity, 3D geometry, and conformational entropy. We chose thiocillin as a model system, a thiopeptide in the ribosomally encoded family of natural products that exhibits potent antimicrobial effects against Gram-positive bacteria. Since thiocillin is derived from a genetically encoded peptide scaffold, site-directed mutagenesis allows for rapid generation of analogues. To understand thiocillin's structure-activity relationship, we generated a site-saturation mutagenesis library covering each position along thiocillin's macrocyclic ring. We report the identification of eight unique compounds more potent than wild-type thiocillin, the best having an 8-fold improvement in potency. Computational modeling of thiocillin's macrocyclic structure revealed a striking requirement for a low-entropy macrocycle for activity. The populated ensembles of the active mutants showed a rigid structure with few adoptable conformations while inactive mutants showed a more flexible macrocycle which is unfavorable for binding. This finding highlights the importance of macrocyclization in combination with rigidifying post-translational modifications to achieve high-potency binding.
Transfer entropy in physical systems and the arrow of time
Spinney, Richard E.; Lizier, Joseph T.; Prokopenko, Mikhail
2016-08-01
Recent developments have cemented the realization that many concepts and quantities in thermodynamics and information theory are shared. In this paper, we consider a highly relevant quantity in information theory and complex systems, the transfer entropy, and explore its thermodynamic role by considering the implications of time reversal upon it. By doing so we highlight the role of information dynamics on the nuanced question of observer perspective within thermodynamics by relating the temporal irreversibility in the information dynamics to the configurational (or spatial) resolution of the thermodynamics. We then highlight its role in perhaps the most enduring paradox in modern physics, the manifestation of a (thermodynamic) arrow of time. We find that for systems that process information such as those undergoing feedback, a robust arrow of time can be formulated by considering both the apparent physical behavior which leads to conventional entropy production and the information dynamics which leads to a quantity we call the information theoretic arrow of time. We also offer an interpretation in terms of optimal encoding of observed physical behavior.
Antibiotic use for irreversible pulpitis.
Agnihotry, Anirudha; Fedorowicz, Zbys; van Zuuren, Esther J; Farman, Allan G; Al-Langawi, Jassim Hasan
2016-02-17
Irreversible pulpitis, which is characterised by acute and intense pain, is one of the most frequent reasons that patients attend for emergency dental care. Apart from removal of the tooth, the customary way of relieving the pain of irreversible pulpitis is by drilling into the tooth, removing the inflamed pulp (nerve) and cleaning the root canal. However, a significant number of dentists continue to prescribe antibiotics to stop the pain of irreversible pulpitis.This review updates the previous version published in 2013. To assess the effects of systemic antibiotics for irreversible pulpitis. We searched the Cochrane Oral Health Group's Trials Register (to 27 January 2016); the Cochrane Central Register of Controlled Trials (CENTRAL) (The Cochrane Library 2015, Issue 12); MEDLINE via Ovid (1946 to 27 January 2016); EMBASE via Ovid (1980 to 27 January 2016), ClinicalTrials.gov (to 27 January 2016) and the WHO International Clinical Trials Registry Platform (to 27 January 2016). There were no language restrictions in the searches of the electronic databases. Randomised controlled trials which compared pain relief with systemic antibiotics and analgesics, against placebo and analgesics in the acute preoperative phase of irreversible pulpitis. Two review authors screened studies and extracted data independently. We assessed the quality of the evidence of included studies using GRADEpro software. Pooling of data was not possible and a descriptive summary is presented. One trial assessed at low risk of bias, involving 40 participants was included in this update of the review. The quality of the body of evidence was rated low for the different outcomes. There was a close parallel distribution of the pain ratings in both the intervention and placebo groups over the seven-day study period. There was insufficient evidence to claim or refute a benefit for penicillin for pain intensity. There was no significant difference in the mean total number of ibuprofen tablets over the
Analysis of thermal systems using the entropy balance method
Energy Technology Data Exchange (ETDEWEB)
Huang, C L.D.; Fartaj, S A; Fenton, D L [Kansas State Univ., Manhattan, KS (United States). Dept. of Mechanical Engineering
1992-04-01
This study investigates the applicability of the second law of thermodynamics using an entropy balance method to analyse and design thermal systems. As examples, the entropy balance method is used to analyse a single stage chiller system and a single stage heat transformer, both with lithium-bromide/water as the working fluid. The entropy method yields not only the same information as is conveyed by the methods of energy and exergy analysis, but it also predicts clearly the influence of irreversibilities of individual components on the coefficient of performance and its effectiveness, based on the process properties, rather than on ambient conditions. Furthermore, this method is capable of presenting the overall distribution of the heat input by displaying the additional heat required to overcome irreversibility of each component without ambiguity. (Author).
Quantum mechanical irreversibility and measurement
Grigolini, P
1993-01-01
This book is intended as a tutorial approach to some of the techniques used to deal with quantum dissipation and irreversibility, with special focus on their applications to the theory of measurements. The main purpose is to provide readers without a deep expertise in quantum statistical mechanics with the basic tools to develop a critical judgement on whether the major achievements in this field have to be considered a satisfactory solution of quantum paradox, or rather this ambitious achievement has to be postponed to when a new physics, more general than quantum and classical physics, will
Entropy Generation in a Chemical Reaction
Miranda, E. N.
2010-01-01
Entropy generation in a chemical reaction is analysed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic equation of an elementary first-order reaction is used to show that entropy production is always positive. A…
Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics.
Glavatskiy, K S
2015-05-28
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.
Li, Shu-Nan; Cao, Bing-Yang
2017-09-01
The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.
Quantum dynamical entropy revisited
International Nuclear Information System (INIS)
Hudetz, T.
1996-10-01
We define a new quantum dynamical entropy, which is a 'hybrid' of the closely related, physically oriented entropy introduced by Alicki and Fannes in 1994, and of the mathematically well-developed, single-argument entropy introduced by Connes, Narnhofer and Thirring in 1987. We show that this new quantum dynamical entropy has many properties similar to the ones of the Alicki-Fannes entropy, and also inherits some additional properties from the CNT entropy. In particular, the 'hybrid' entropy interpolates between the two different ways in which both the AF and the CNT entropy of the shift automorphism on the quantum spin chain agree with the usual quantum entropy density, resulting in even better agreement. Also, the new quantum dynamical entropy generalizes the classical dynamical entropy of Kolmogorov and Sinai in the same way as does the AF entropy. Finally, we estimate the 'hybrid' entropy both for the Powers-Price shift systems and for the noncommutative Arnold map on the irrational rotation C * -algebra, leaving some interesting open problems. (author)
Directory of Open Access Journals (Sweden)
Urban Kordes
2005-10-01
Full Text Available The paper tries to tackle the question of connection between entropy and the living. Definitions of life as the phenomenon that defies entropy are overviewed and the conclusion is reached that life is in a way dependant on entropy - it couldn't exist without it. Entropy is a sort of medium, a fertile soil, that gives life possibility to blossom. Paper ends with presenting some consequences for the field of artificial intelligence.
Entropy of Baker's Transformation
Institute of Scientific and Technical Information of China (English)
栾长福
2003-01-01
Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.
Ben-Naim, Arieh
2011-01-01
Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)
Irreversible Thermodynamics of the Universe: Constraints from Planck Data
International Nuclear Information System (INIS)
Saha, Subhajit; Chakraborty, Subenoy; Biswas, Atreyee
2014-01-01
The present work deals with irreversible universal thermodynamics. The homogenous and isotropic flat model of the universe is chosen as open thermodynamical system and nonequilibrium thermodynamics comes into picture. For simplicity, entropy flow is considered only due to heat conduction. Further, due to Maxwell-Cattaneo modified Fourier law for nonequilibrium phenomenon, the temperature satisfies damped wave equation instead of heat conduction equation. Validity of generalized second law of thermodynamics (GSLT) has been investigated for universe bounded by apparent or event horizon with cosmic substratum as perfect fluid with constant or variable equation of state or interacting dark species. Finally, we have used three Planck data sets to constrain the thermal conductivity λ and the coupling parameter b 2 . These constraints must be satisfied in order for GSLT to hold for universe bounded by apparent or event horizons
Thermodynamic Optimality criteria for biological systems in linear irreversible thermodynamics
International Nuclear Information System (INIS)
Chimal, J C; Sánchez, N; Ramírez, PR
2017-01-01
In this paper the methodology of the so-called Linear Irreversible Thermodynamics (LIT) is applied; although traditionally used locally to study general systems in non-equilibrium states in which it is consider both internal and external contributions to the entropy increments in order to analyze the efficiency of two coupled processes with generalized fluxes J 1 , J 2 and their corresponding forces X 1 , X 2 . We extend the former analysis to takes into account two different operating regimes namely: Omega Function and Efficient Power criterion, respectively. Results show analogies in the optimal performance between and we can say that there exist a criteria of optimization which can be used specially for biological systems where a good design of the biological parameters made by nature at maximum efficient power conditions lead to more efficient engines than those at the maximum power conditions or ecological conditions. (paper)
International Nuclear Information System (INIS)
Sieniutycz, S.; Berry, R.S.
1993-01-01
A Lagrangian with dissipative (e.g., Onsager's) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is ''To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum?'' Noether's energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy E, it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as ''irreversible'' (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy
Quantum entropy of systems described by non-Hermitian Hamiltonians
International Nuclear Information System (INIS)
Sergi, Alessandro; Zloshchastiev, Konstantin G
2016-01-01
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non-Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one can consider the generalized entropy as the informational entropy describing the flow of information between the system and the bath. We illustrate the theory by explicitly studying few simple models, including tunneling systems with two energy levels and non-Hermitian detuning. (paper: quantum statistical physics, condensed matter, integrable systems)
Gravitational entropies in LTB dust models
International Nuclear Information System (INIS)
Sussman, Roberto A; Larena, Julien
2014-01-01
We consider generic Lemaître–Tolman–Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non-local domain dependent manner for the two HB proposals. By looking at the fulfilment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to a Friedmann–Lemaître–Robertson–Walker background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a ‘gravitational entropy’ may be a theoretically robust concept applicable to more general spacetimes. (paper)
Volkenstein, Mikhail V
2009-01-01
The book "Entropy and Information" deals with the thermodynamical concept of entropy and its relationship to information theory. It is successful in explaining the universality of the term "Entropy" not only as a physical phenomenon, but reveals its existence also in other domains. E.g., Volkenstein discusses the "meaning" of entropy in a biological context and shows how entropy is related to artistic activities. Written by the renowned Russian bio-physicist Mikhail V. Volkenstein, this book on "Entropy and Information" surely serves as a timely introduction to understand entropy from a thermodynamic perspective and is definitely an inspiring and thought-provoking book that should be read by every physicist, information-theorist, biologist, and even artist.
RNA Thermodynamic Structural Entropy.
Garcia-Martin, Juan Antonio; Clote, Peter
2015-01-01
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
RNA Thermodynamic Structural Entropy.
Directory of Open Access Journals (Sweden)
Juan Antonio Garcia-Martin
Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
Anomalies, Unitarity and Quantum Irreversibility
Anselmi, D
1999-01-01
The trace anomaly in external gravity is the sum of three terms at criticality: the square of the Weyl tensor, the Euler density and Box R, with coefficients, properly normalized, called c, a and a', the latter being ambiguously defined by an additive constant. Unitarity and positivity properties of the induced actions allow us to show that the total RG flows of a and a' are equal and therefore the a'-ambiguity can be consistently removed through the identification a'=a. The picture that emerges clarifies several long-standing issues. The interplay between unitarity and renormalization implies that the flux of the renormalization group is irreversible. A monotonically decreasing a-function interpolating between the appropriate values is naturally provided by a'. The total a-flow is expressed non-perturbatively as the invariant (i.e. scheme-independent) area of the graph of the beta function between the fixed points. We test this prediction to the fourth loop order in perturbation theory, in QCD with Nf ~< ...
International Nuclear Information System (INIS)
Polettini, Matteo; Esposito, Massimiliano
2014-01-01
In this paper and Paper II, we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated with nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation a + b = s Y between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats s Y . We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction
Polettini, Matteo; Esposito, Massimiliano
2014-07-14
In this paper and Paper II, we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated with nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation a + b = s(Y) between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats s(Y). We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction.
Examination of various postulates of irreversibility
Energy Technology Data Exchange (ETDEWEB)
Salmon, J [Conservatoire National des Arts et Metiers (CNAM), 75 - Paris (France)
1977-01-01
Firstly, it is shown that it is necessary to break the reversible character of the B.B.G.K.Y. system of equations by means of a postulate of irreversibility to obtain a kinetic equation compatible with the second principle of thermodynamics. Next, three postulates of irreversibility are examined: that of molecular chaos, that of linear relaxation and, finally, that of superposition. Then the corresponding kinetic equations and the expressions for the viscosity coefficient to which they lead are determined. Comparison with experiment is made each time. Lastly, an attempt to obtain an irreversible kinetic equation without introducing a postulate of irreversibility in the B.B.G.K.Y. system is realized. This consists in adding a complementary irreversible term to the fundamental equation of the dynamics of a particle. The suggested term is of quantum origin and leads to a kinetic equation of the Fokker-Planck type.
Directory of Open Access Journals (Sweden)
Budi Santosa
2016-01-01
Full Text Available This paper presents a model and an algorithm for an inventory ship routing problem (ISRP. It consists of two main parts: a model development of the ship routing problem in a multi-product inventory with a heterogeneous fleet and an algorithm development to solve the problem. The problem is referred to as ISRP. ISRP considers several parameters including the deadweight tonnage (DWT, product compatibility, port setup, and compartment washing costs. Considering these parameters, the objective function is to minimize the total cost, which consists of traveling, port setup, ship charter, and compartment washing costs. From the resulting model, there are two major steps used to solve the problem. The first is to select the ships in order to satisfy the constraint that restricts the mooring rule. The second is to find the best route, product allocation, and shipped quantity. ISRP is an Non Polynomial-hard problem. Finding the solution of such problem needs a high computation time. A new hybrid metaheuristics, namely the cross entropy-genetic algorithm (CEGA, was proposed to solve ISRP. The results were then compared with those resulted from a hybrid Tabu Search to measure the hybrid CEGA performance. The results showed that CEGA provided better solutions than those produced by the hybrid Tabu Search.
Energy Technology Data Exchange (ETDEWEB)
Açıkkalp, Emin, E-mail: eacikkalp@gmail.com [Department of Mechanical and Manufacturing Engineering, Engineering Faculty, Bilecik S.E. University, Bilecik (Turkey); Caner, Necmettin [Department of Chemistry, Faculty of Arts and Sciences, Eskisehir Osmangazi University, Eskisehir (Turkey)
2015-09-25
Highlights: • An irreversible Brayton cycle operating quantum gasses is considered. • Exergetic sustainability index is derived for nano-scale cycles. • Nano-scale effects are considered. • Calculation are conducted for irreversible cycles. • Numerical results are presented and discussed. - Abstract: In this study, a nano-scale irreversible Brayton cycle operating with quantum gasses including Bose and Fermi gasses is researched. Developments in the nano-technology cause searching the nano-scale machines including thermal systems to be unavoidable. Thermodynamic analysis of a nano-scale irreversible Brayton cycle operating with Bose and Fermi gasses was performed (especially using exergetic sustainability index). In addition, thermodynamic analysis involving classical evaluation parameters such as work output, exergy output, entropy generation, energy and exergy efficiencies were conducted. Results are submitted numerically and finally some useful recommendations were conducted. Some important results are: entropy generation and exergetic sustainability index are affected mostly for Bose gas and power output and exergy output are affected mostly for the Fermi gas by x. At the high temperature conditions, work output and entropy generation have high values comparing with other degeneracy conditions.
Watson, Andrew B.; Stone, Leland (Technical Monitor)
1997-01-01
) an Arts and Letters emphasis, and c) a Computer Science emphasis Each pathway includes course work in remote sensing, geographical information systems (GIS), computer science, Earth science, software and technology utilization, and communication. Distribution of products from this project to other two-year colleges will be accomplished using the WWW.
Maximum Quantum Entropy Method
Sim, Jae-Hoon; Han, Myung Joon
2018-01-01
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input matrix. As a result, the continuation of off-diagonal elements becomes straightforward. Without introducing any further ambiguity, the Bayesian probabilistic interpretation is maintained just as in the conventional maximum entropy method. The applications o...
Transplanckian entanglement entropy
International Nuclear Information System (INIS)
Chang, Darwin; Chu, C.-S.; Lin Fengli
2004-01-01
The entanglement entropy of the event horizon is known to be plagued by the UV divergence due to the infinitely blue-shifted near horizon modes. In this Letter we calculate the entanglement entropy using the transplanckian dispersion relation, which has been proposed to model the quantum gravity effects. We show that, very generally, the entropy is rendered UV finite due to the suppression of high energy modes effected by the transplanckian dispersion relation
2015-09-29
antiferroelectrics. Phys. Rev. Lett. 110, 017603 (2013). 22. Cantor , B., Chang, I., Knight, P. & Vincent, A. Microstructural development in equiatomic...Science 345, 1153–1158 (2014). 24. Gali, A. & George , E. Tensile properties of high- and medium-entropy alloys. Intermetallics 39, 74–78 (2013). 25...148–153 (2014). 26. Otto, F., Yang, Y., Bei, H. & George , E. Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc
2011-05-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan
2011-01-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY
Institute of Scientific and Technical Information of China (English)
M. Rahimi A. Riazi
2012-01-01
In this article,we introduce the concept of entropy functional for continuous systems on compact metric spaces,and prove some of its properties.We also extract the Kolmogorov entropy from the entropy functional.
The Elusive Nature of Entropy and Its Physical Meaning
Directory of Open Access Journals (Sweden)
Milivoje M. Kostic
2014-02-01
Full Text Available Entropy is the most used and often abused concept in science, but also in philosophy and society. Further confusions are produced by some attempts to generalize entropy with similar but not the same concepts in other disciplines. The physical meaning of phenomenological, thermodynamic entropy is reasoned and elaborated by generalizing Clausius definition with inclusion of generated heat, since it is irrelevant if entropy is changed due to reversible heat transfer or irreversible heat generation. Irreversible, caloric heat transfer is introduced as complementing reversible heat transfer. It is also reasoned and thus proven why entropy cannot be destroyed but is always generated (and thus over-all increased locally and globally, at every space and time scales, without any exception. It is concluded that entropy is a thermal displacement (dynamic thermal-volume of thermal energy due to absolute temperature as a thermal potential (dQ = TdS, and thus associated with thermal heat and absolute temperature, i.e., distribution of thermal energy within thermal micro-particles in space. Entropy is an integral measure of (random thermal energy redistribution (due to heat transfer and/or irreversible heat generation within a material system structure in space, per absolute temperature level: dS = dQSys/T = mCSysdT/T, thus logarithmic integral function, with J/K unit. It may be also expressed as a measure of “thermal disorder”, being related to logarithm of number of all thermal, dynamic microstates W (their position and momenta, S = kBlnW, or to the sum of their logarithmic probabilities S = −kB∑pilnpi, that correspond to, or are consistent with the given thermodynamic macro-state. The number of thermal microstates W, is correlated with macro-properties temperature T and volume V for ideal gases. A system form and/or functional order or disorder are not (thermal energy order/disorder and the former is not related to Thermodynamic entropy. Expanding
Numerical analysis of entropy generation in an annular microcombustor using multistep kinetics
International Nuclear Information System (INIS)
Jejurkar, Swarup Y.; Mishra, D.P.
2013-01-01
Entropy generation by combustion and additional irreversibility due to heat loss was studied numerically for a premixed flame based microcombustor. Detailed axisymmetric reactive flow model employing a 21 step–9 species reaction mechanism for hydrogen–air mixture was considered. The analysis identified reactions contributing most of the entropy generated in combustion. These reactions are removed from thermodynamic equilibrium in the low temperature region between 400 and 700 K of the flame and a combination of their high affinity and low temperature induces entropy generation in this region. Single step kinetics and a reduced scheme neglecting HO 2 is consequently incapable of accurately calculating the entropy generation and second law performance. Overall entropy generation rates increased from lean to rich mixtures in the range Φ = 0.5–1.4 and were dominated by combustion reactions. Characterization of combustor performance in terms of second law efficiency showed that availability reduction by wall heat losses and combustion irreversibility were of the same order for stoichiometric and both decreased for rich flames. On the other hand, near-quenching fuel lean flames (Φ≤0.75) suffered mostly from combustion irreversibility. These trends caused the minimum efficiency (maximum thermodynamic irreversibility) point to locate near stoichiometric fuel–air composition. -- Highlights: ► Reaction set dominating heat release and entropy generation involve HO 2 . ► Entropy generation increased from lean to rich Φ. ► Second law efficiency is minimum at stoichiometric Φ. ► Post-flame heat loss, transport processes needed in microcombustor entropy analysis
Optimization of an irreversible Stirling regenerative cycle
International Nuclear Information System (INIS)
Aragón-González, G; Cano-Bianco, M; León-Galicia, A; Rivera-Camacho, J M
2015-01-01
In this work a Stirling regenerative cycle with some irreversibilities is analyzed. The analyzed irreversibilities are located at the heat exchangers. They receive a finite amount of heat and heat leakage occurs between both reservoirs. Using this model, power and the efficiency at maximum power are obtained. Some optimal design parameters for the exchanger heat areas and thermal conductances are presented. The relation between the power, efficiency and the results obtained are shown graphically
Irreversible thermodynamics of Poisson processes with reaction.
Méndez, V; Fort, J
1999-11-01
A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics.
Indian Academy of Sciences (India)
Enthalpy–entropy compensation is the name given to the correlation sometimes observed between the estimates of the enthalpy and entropy of a reaction obtained from temperature-dependence data. Although the mainly artefactual nature of this correlation has been known for many years, the subject enjoys periodical ...
Indian Academy of Sciences (India)
During the process of ageing, the balance shifts in the direction of anarchy. Death is ... tion of life and the laws of statistieal physics and entropy, both of which ... capable of doing work. ... defined by Ludwig Boltzmann in 1877, the entropy of the.
Energy Technology Data Exchange (ETDEWEB)
Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Nezami, Sepehr [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Ooguri, Hirosi [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa 277-8583 (Japan); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory, Stanford University,Menlo Park, CA 94025 (United States); Walter, Michael [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2015-09-21
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
International Nuclear Information System (INIS)
Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael
2015-01-01
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
Entropy and Digital Installation
Directory of Open Access Journals (Sweden)
Susan Ballard
2005-01-01
Full Text Available This paper examines entropy as a process which introduces ideas of distributed materiality to digital installation. Beginning from an analysis of entropy as both force and probability measure within information theory and it’s extension in Ruldof Arnheim’s text ‘Entropy and Art” it develops an argument for the positive rather thannegative forces of entropy. The paper centres on a discussion of two recent works by New Zealand artists Ronnie van Hout (“On the Run”, Wellington City Gallery, NZ, 2004 and Alex Monteith (“Invisible Cities”, Physics Room Contemporary Art Space, Christchurch, NZ, 2004. Ballard suggests that entropy, rather than being a hindrance to understanding or a random chaotic force, discloses a necessary and material politics of noise present in digital installation.
Linear entropy in quantum phase space
International Nuclear Information System (INIS)
Rosales-Zarate, Laura E. C.; Drummond, P. D.
2011-01-01
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
Linear entropy in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Rosales-Zarate, Laura E. C.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)
2011-10-15
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
Nonsymmetric entropy I: basic concepts and results
Liu, Chengshi
2006-01-01
A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally from maximal nonsymmetric entropy principle.
Entanglement entropy and nonabelian gauge symmetry
International Nuclear Information System (INIS)
Donnelly, William
2014-01-01
Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang–Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity. (paper)
Entropy Generation in Natural Convection Under an Evanescent Magnetic Field
International Nuclear Information System (INIS)
Magherbi, Mourad; El Jery, Atef; Ben Brahim, Ammar
2009-01-01
We numerically study the effect of an externally-evanescent magnetic field on total entropy generation in conducting and non-reactive fluid enclosed in a square cavity. The horizontal walls of the enclosure are assumed to be insulated while the vertical walls are kept isothermal. A control volume finite element method is used to solve the conservation equations at Prandtl number of 0.71. The values of relaxation time of the magnetic field are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. The total entropy generation was calculated for fixed value of irreversibility distribution ratio, different relaxation time varying from 0 to 1/5 and Grashof number equal to 10 5
Entropy of the Mixture of Sources and Entropy Dimension
Smieja, Marek; Tabor, Jacek
2011-01-01
We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.
Entropy coherent and entropy convex measures of risk
Laeven, Roger; Stadje, M.A.
2010-01-01
We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized
Entropy coherent and entropy convex measures of risk
Laeven, R.J.A.; Stadje, M.
2013-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex
Entropy Coherent and Entropy Convex Measures of Risk
Laeven, R.J.A.; Stadje, M.A.
2011-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences,
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2013-01-01
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)
Black hole thermodynamical entropy
International Nuclear Information System (INIS)
Tsallis, Constantino; Cirto, Leonardo J.L.
2013-01-01
As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy S BG of a (3+1) black hole is proportional to its area L 2 (L being a characteristic linear length), and not to its volume L 3 . Similarly it exists the area law, so named because, for a wide class of strongly quantum-entangled d-dimensional systems, S BG is proportional to lnL if d=1, and to L d-1 if d>1, instead of being proportional to L d (d ≥ 1). These results violate the extensivity of the thermodynamical entropy of a d-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is not to be identified with the BG additive entropy but with appropriately generalized nonadditive entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle. (orig.)
Is thermodynamic irreversibility a consequence of the expansion of the Universe?
Osváth, Szabolcs
2018-02-01
This paper explains thermodynamic irreversibility by applying the expansion of the Universe to thermodynamic systems. The effect of metric expansion is immeasurably small on shorter scales than intergalactic distances. Multi-particle systems, however, are chaotic, and amplify any small disturbance exponentially. Metric expansion gives rise to time-asymmetric behaviour in thermodynamic systems in a short time (few nanoseconds in air, few ten picoseconds in water). In contrast to existing publications, this paper explains without any additional assumptions the rise of thermodynamic irreversibility from the underlying reversible mechanics of particles. Calculations for the special case which assumes FLRW metric, slow motions (v ≪ c) and approximates space locally by Euclidean space show that metric expansion causes entropy increase in isolated systems. The rise of time-asymmetry, however, is not affected by these assumptions. Any influence of the expansion of the Universe on the local metric causes a coupling between local mechanics and evolution of the Universe.
Ecological optimization and performance study of irreversible Stirling and Ericsson heat engines
International Nuclear Information System (INIS)
Tyagi, S K; Kaushik, S C; Salhotra, R
2002-01-01
The concept of finite time thermodynamics is used to determine the ecological function of irreversible Stirling and Ericsson heat engine cycles. The ecological function is defined as the power output minus power loss (irreversibility), which is the ambient temperature times, the entropy generation rate. The ecological function is maximized with respect to cycle temperature ratio and the expressions for the corresponding power output and thermal efficiency are derived at the optimal operating conditions. The effect of different operating parameters, the effectiveness on the hot, cold and the regenerative side heat exchangers, the cycle temperature ratio, heat capacitance ratio and the internal irreversibility parameter on the maximum ecological function are studied. It is found that the effect of regenerator effectiveness is more than the hot and cold side heat exchangers and the effect of the effectiveness on cold side heat exchanger is more than the effectiveness on the hot side heat exchanger on the maximum ecological function. It is also found that the effect of internal irreversibility parameter is more than the other parameters not only on the maximum ecological function but also on the corresponding power output and the thermal efficiency
Ecological optimization and performance study of irreversible Stirling and Ericsson heat engines
Tyagi, S. K.; Kaushik, S. C.; Salhotra, R.
2002-10-01
The concept of finite time thermodynamics is used to determine the ecological function of irreversible Stirling and Ericsson heat engine cycles. The ecological function is defined as the power output minus power loss (irreversibility), which is the ambient temperature times, the entropy generation rate. The ecological function is maximized with respect to cycle temperature ratio and the expressions for the corresponding power output and thermal efficiency are derived at the optimal operating conditions. The effect of different operating parameters, the effectiveness on the hot, cold and the regenerative side heat exchangers, the cycle temperature ratio, heat capacitance ratio and the internal irreversibility parameter on the maximum ecological function are studied. It is found that the effect of regenerator effectiveness is more than the hot and cold side heat exchangers and the effect of the effectiveness on cold side heat exchanger is more than the effectiveness on the hot side heat exchanger on the maximum ecological function. It is also found that the effect of internal irreversibility parameter is more than the other parameters not only on the maximum ecological function but also on the corresponding power output and the thermal efficiency.
Irreversibility and self-organization in spin glasses. 1. Origin of irreversibility in spin glasses
International Nuclear Information System (INIS)
Kovrov, V.P.; Kurbatov, A.M.
1989-05-01
The origin of irreversibility in spin glasses is found out on the basis of the analytical study of the well-known TAP equations. Connection between irreversible jumpwise transitions and a positive feedback in spin glasses is discussed. (author). 7 refs, 4 figs
On the generalized entropy pseudoadditivity for complex systems
International Nuclear Information System (INIS)
Wang, Qiuping A.; Nivanen, Laurent; Le Mehaute, Alain; Pezeril, Michel
2002-01-01
We show that Abe's general pseudoadditivity for entropy prescribed by thermal equilibrium in nonextensive systems holds not only for entropy, but also for energy. The application of this general pseudoadditivity to Tsallis entropy tells us that the factorization of the probability of a composite system into a product of the probabilities of the subsystems is just a consequence of the existence of thermal equilibrium and not due to the independence of the subsystems. (author)
Some remarks on conditional entropy
Nijst, A.G.P.M.
1969-01-01
Using a definition of conditional entropy given by Hanen and Neveu [5, 10, 11] we discuss in this paper some properties of conditional entropy and mean entropy, in particular an integral representation of conditional entropy (§ 2), and the decomposition theorem of the KolmogorovSina¯i invariant (§
International Nuclear Information System (INIS)
Estes, John; Jensen, Kristan; O’Bannon, Andy; Tsatis, Efstratios; Wrase, Timm
2014-01-01
We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions
Katan, Claudine; Mohite, Aditya D.; Even, Jacky
2018-05-01
Claudine Katan, Aditya D. Mohite and Jacky Even discuss the possible impact of various entropy contributions (stochastic structural fluctuations, anharmonicity and lattice softness) on the optoelectronic properties of halide perovskite materials and devices.
International Nuclear Information System (INIS)
Rangel-Hernandez, V.H.; Damian-Ascencio, C.; Juarez-Robles, D.; Gallegos-Munoz, A.; Zaleta-Aguilar, A.; Plascencia-Mora, H.
2011-01-01
The present paper aims at investigating the main sources of irreversibility in a Proton Exchange Membrane Fuel Cell (PEMFC) using a Fermat spiral as flow distributor and also to direct possible improvements in its design. The numerical analysis is based on a finite volume technique with a SIMPLE algorithm as numerical procedure. In order to have a more complete and rigorous analysis a new dimensionless parameter is proposed here. The parameter represents the ratio of the entropy generation due to mass transfer to the total entropy generation is proposed here. Results demonstrate that the main sources of irreversibility in a fuel cell are the concentration losses for the most part of the operational domain, whereas the heat transfer effect is not dominant. -- Highlights: → PEM Fuel Cell with Fermat Spiral as distributor. → Causes of irreversibilities. → A new dimensionless parameter to determine contribution of mass transfer in entropy generation.
Sze, Vivienne; Marpe, Detlev
2014-01-01
Context-Based Adaptive Binary Arithmetic Coding (CABAC) is a method of entropy coding first introduced in H.264/AVC and now used in the latest High Efficiency Video Coding (HEVC) standard. While it provides high coding efficiency, the data dependencies in H.264/AVC CABAC make it challenging to parallelize and thus limit its throughput. Accordingly, during the standardization of entropy coding for HEVC, both aspects of coding efficiency and throughput were considered. This chapter describes th...
Manfredi; Feix
2000-10-01
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.
Manfredi, G.; Feix, M. R.
2002-01-01
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functions
Feasible Histories, Maximum Entropy
International Nuclear Information System (INIS)
Pitowsky, I.
1999-01-01
We consider the broadest possible consistency condition for a family of histories, which extends all previous proposals. A family that satisfies this condition is called feasible. On each feasible family of histories we choose a probability measure by maximizing entropy, while keeping the probabilities of commuting histories to their quantum mechanical values. This procedure is justified by the assumption that decoherence increases entropy. Finally, a criterion for identifying the nearly classical families is proposed
Gulamsarwar, Syazwani; Salleh, Zabidin
2017-08-01
The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.
Solutions to the Cosmic Initial Entropy Problem without Equilibrium Initial Conditions
Directory of Open Access Journals (Sweden)
Vihan M. Patel
2017-08-01
Full Text Available The entropy of the observable universe is increasing. Thus, at earlier times the entropy was lower. However, the cosmic microwave background radiation reveals an apparently high entropy universe close to thermal and chemical equilibrium. A two-part solution to this cosmic initial entropy problem is proposed. Following Penrose, we argue that the evenly distributed matter of the early universe is equivalent to low gravitational entropy. There are two competing explanations for how this initial low gravitational entropy comes about. (1 Inflation and baryogenesis produce a virtually homogeneous distribution of matter with a low gravitational entropy. (2 Dissatisfied with explaining a low gravitational entropy as the product of a ‘special’ scalar field, some theorists argue (following Boltzmann for a “more natural” initial condition in which the entire universe is in an initial equilibrium state of maximum entropy. In this equilibrium model, our observable universe is an unusual low entropy fluctuation embedded in a high entropy universe. The anthropic principle and the fluctuation theorem suggest that this low entropy region should be as small as possible and have as large an entropy as possible, consistent with our existence. However, our low entropy universe is much larger than needed to produce observers, and we see no evidence for an embedding in a higher entropy background. The initial conditions of inflationary models are as natural as the equilibrium background favored by many theorists.
International Nuclear Information System (INIS)
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2010-01-01
We trace the origin of the black hole entropy S, replacing a black hole by a quasiblack hole. Let the boundary of a static body approach its own gravitational radius, in such a way that a quasihorizon forms. We show that if the body is thermal with the temperature taking the Hawking value at the quasihorizon limit, it follows, in the nonextremal case, from the first law of thermodynamics that the entropy approaches the Bekenstein-Hawking value S=A/4. In this setup, the key role is played by the surface stresses on the quasihorizon and one finds that the entropy comes from the quasihorizon surface. Any distribution of matter inside the surface leads to the same universal value for the entropy in the quasihorizon limit. This can be of some help in the understanding of black hole entropy. Other similarities between black holes and quasiblack holes such as the mass formulas for both objects had been found previously. We also discuss the entropy for extremal quasiblack holes, a more subtle issue.
On the Conditional Rényi Entropy
S. Fehr (Serge); S. Berens (Stefan)
2014-01-01
htmlabstractThe Rényi entropy of general order unifies the well-known Shannon entropy with several other entropy notions, like the min-entropy or the collision entropy. In contrast to the Shannon entropy, there seems to be no commonly accepted definition for the conditional Rényi entropy: several
Ellipses of constant entropy in the XY spin chain
International Nuclear Information System (INIS)
Franchini, F; Its, A R; Jin, B-Q; Korepin, V E
2007-01-01
Entanglement in the ground state of the XY model on the infinite chain can be measured by the von Neumann entropy of a block of neighbouring spins. We study a double scaling limit: the size of the block is much larger than 1 but much smaller than the length of the whole chain. The entropy of the block has an asymptotic limit in the gapped regimes. We study this limiting entropy as a function of the anisotropy and of the magnetic field. We identify its minima at product states and its divergencies at the quantum phase transitions. We find that the curves of constant entropy are ellipses and hyperbolas, and that they all meet at one point (essential critical point). Depending on the approach to the essential critical point, the entropy can take any value between 0 and ∞. In the vicinity of this point, small changes in the parameters cause large change of the entropy
Absorption media for irreversibly gettering thionyl chloride
Buffleben, George; Goods, Steven H.; Shepodd, Timothy; Wheeler, David R.; Whinnery, Jr., LeRoy
2002-01-01
Thionyl chloride is a hazardous and reactive chemical used as the liquid cathode in commercial primary batteries. Contrary to previous thinking, ASZM-TEDA.RTM. carbon (Calgon Corporation) reversibly absorbs thionyl chloride. Thus, several candidate materials were examined as irreversible getters for thionyl chloride. The capacity, rate and effect of temperature were also explored. A wide variety of likely materials were investigated through screening experiments focusing on the degree of heat generated by the reaction as well as the material absorption capacity and irreversibility, in order to help narrow the group of possible getter choices. More thorough, quantitative measurements were performed on promising materials. The best performing getter was a mixture of ZnO and ASZM-TEDA.RTM. carbon. In this example, the ZnO reacts with thionyl chloride to form ZnCl.sub.2 and SO.sub.2. The SO.sub.2 is then irreversibly gettered by ASZM-TEDA.RTM. carbon. This combination of ZnO and carbon has a high capacity, is irreversible and functions effectively above -20.degree. C.
Risk Aversion, Price Uncertainty and Irreversible Investments
van den Goorbergh, R.W.J.; Huisman, K.J.M.; Kort, P.M.
2003-01-01
This paper generalizes the theory of irreversible investment under uncertainty by allowing for risk averse investors in the absence of com-plete markets.Until now this theory has only been developed in the cases of risk neutrality, or risk aversion in combination with complete markets.Within a
Port contact systems for irreversible thermodynamical systems
Eberard, D.; Maschke, B.M.; Schaft, A.J. van der
2005-01-01
In this paper we propose a definition of control contact systems, generalizing input-output Hamiltonian systems, to cope with models arising from irreversible Thermodynamics. We exhibit a particular subclass of these systems, called conservative, that leaves invariant some Legendre submanifold (the
Onsager's reciprocity theorem in extended irreversible thermodynamics
International Nuclear Information System (INIS)
Garcia-Colin, L.S.; Velasco, R.M.
1992-01-01
In this paper we shall discuss the Onsager relations for the transport coefficients in a dilute monatomic gas described by the extended irreversible thermodynamics. Our discussion is based on a 26 variables description of the system and its corresponding comparison with the kinetic reciprocity between coefficients is shown (Author)
A kinetic equation for irreversible aggregation
International Nuclear Information System (INIS)
Zanette, D.H.
1990-09-01
We introduce a kinetic equation for describing irreversible aggregation in the ballistic regime, including velocity distributions. The associated evolution for the macroscopic quantities is studied, and the general solution for Maxwell interaction models is obtained in the Fourier representation. (author). 23 refs
EEG entropy measures in anesthesia
Directory of Open Access Journals (Sweden)
Zhenhu eLiang
2015-02-01
Full Text Available Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs’ effect is lacking. In this study, we compare the capability of twelve entropy indices for monitoring depth of anesthesia (DoA and detecting the burst suppression pattern (BSP, in anesthesia induced by GA-BAergic agents.Methods: Twelve indices were investigated, namely Response Entropy (RE and State entropy (SE, three wavelet entropy (WE measures (Shannon WE (SWE, Tsallis WE (TWE and Renyi WE (RWE, Hilbert-Huang spectral entropy (HHSE, approximate entropy (ApEn, sample entropy (SampEn, Fuzzy entropy, and three permutation entropy (PE measures (Shannon PE (SPE, Tsallis PE (TPE and Renyi PE (RPE. Two EEG data sets from sevoflurane-induced and isoflu-rane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, phar-macokinetic / pharmacodynamic (PK/PD modeling and prediction probability analysis were applied. The multifractal detrended fluctuation analysis (MDFA as a non-entropy measure was compared.Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline vari-ability, higher coefficient of determination and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an ad-vantage in computation efficiency compared with MDFA.Conclusion: Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure.Significance: Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.
Lambarraa, Fatima; Stefanou, Spiro; Gil, José M.
2016-01-01
This study addresses irreversible investment decision-making in the context of uncertainty when allowing for inefficiency to be transmitted over time. Both irreversibility and persistence in technical inefficiency can lead to sluggish adjustment of quasi-fixed factors of production. The context
Buchkremer, S.; Klocke, F.
2017-01-01
Performance and operational safety of many metal parts in engineering depend on their surface integrity. During metal cutting, large thermomechanical loads and high gradients of the loads concerning time and location act on the surfaces and may yield significant structural material modifications, which alter the surface integrity. In this work, the derivation and validation of a model of nanostructural surface modifications in metal cutting are presented. For the first time in process modeling, initiation and kinetics of these modifications are predicted using a thermodynamic potential, which considers the interdependent developments of plastic work, dissipation, heat conduction and interface energy as well as the associated productions and flows of entropy. The potential is expressed based on the free Helmholtz energy. The irreversible thermodynamic state changes in the workpiece surface are homogenized over the volume in order to bridge the gap between discrete phenomena involved with the initiation and kinetics of dynamic recrystallization and its macroscopic implications for surface integrity. The formulation of the thermodynamic potential is implemented into a finite element model of orthogonal cutting of steel AISI 4140. Close agreement is achieved between predicted nanostructures and those obtained in transmission electron microscopical investigations of specimen produced in cutting experiments.
Directory of Open Access Journals (Sweden)
Qinglin Cheng
2018-04-01
Full Text Available With the increasing demand of oil products in China, the energy consumption of pipeline operation will continue to rise greatly, as well as the cost of oil transportation. In the field of practical engineering, saving energy, reducing energy consumption and adapting to the international oil situation are the development trends and represent difficult problems. Based on the basic principle of non-equilibrium thermodynamics, this paper derives the field equilibrium equations of non-equilibrium thermodynamic process for pipeline transportation. To seek the bilinear form of “force” and “flow” in the non-equilibrium thermodynamics of entropy generation rate, the oil pipeline exergy balance equation and the exergy transfer pipeline dynamic equation of the irreversibility were established. The exergy balance equation was applied to energy balance evaluation system, which makes the system more perfect. The exergy flow transfer law of the waxy oil pipeline were explored deeply from the directions of dynamic exergy, pressure exergy, thermal exergy and diffusion exergy. Taking an oil pipeline as an example, the influence factors of exergy transfer coefficient and exergy flow density were analyzed separately.
International Nuclear Information System (INIS)
Kovrov, V.P.; Kurbatov, A.M.
1989-05-01
The generalization of a configuration averaging to a system displaying irreversible effects is suggested. The properties of the ''pathological'' equilibrium state at low temperatures are determined and discussed. (author). 16 refs, 3 figs
Bianconi, Ginestra
2009-03-01
In this paper we generalize the concept of random networks to describe network ensembles with nontrivial features by a statistical mechanics approach. This framework is able to describe undirected and directed network ensembles as well as weighted network ensembles. These networks might have nontrivial community structure or, in the case of networks embedded in a given space, they might have a link probability with a nontrivial dependence on the distance between the nodes. These ensembles are characterized by their entropy, which evaluates the cardinality of networks in the ensemble. In particular, in this paper we define and evaluate the structural entropy, i.e., the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence. We stress the apparent paradox that scale-free degree distributions are characterized by having small structural entropy while they are so widely encountered in natural, social, and technological complex systems. We propose a solution to the paradox by proving that scale-free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy. Finally, the general framework we present in this paper is able to describe microcanonical ensembles of networks as well as canonical or hidden-variable network ensembles with significant implications for the formulation of network-constructing algorithms.
A gravitational entropy proposal
International Nuclear Information System (INIS)
Clifton, Timothy; Tavakol, Reza; Ellis, George F R
2013-01-01
We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy
Gupta; Srivastava
2010-01-01
Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian est...
EEG entropy measures in anesthesia
Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli
2015-01-01
Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation
Optima and bounds for irreversible thermodynamic processes
International Nuclear Information System (INIS)
Hoffmann, K.H.
1990-01-01
In this paper bounds and optima for irreversible thermodynamic processes and their application in different fields are discussed. The tools of finite time thermodynamics are presented and especially optimal control theory is introduced. These methods are applied to heat engines, including models of the Diesel engine and a light-driven engine. Further bounds for irreversible processes are introduced, discussing work deficiency and its relation to thermodynamic length. Moreover the problem of dissipation in systems composed of several subsystems is studied. Finally, the methods of finite time thermodynamics are applied to thermodynamic processes described on a more microscopic level. The process used as an example is simulated annealing. It is shown how optimal control theory is applied to find the optimal cooling schedule for this important stochastic optimization method
Time in Science: Reversibility vs. Irreversibility
Pomeau, Yves
To discuss properly the question of irreversibility one needs to make a careful distinction between reversibility of the equations of motion and the choice of the initial conditions. This is also relevant for the rather confuse philosophy of the wave packet reduction in quantum mechanics. The explanation of this reduction requires also to make precise assumptions on what initial data are accessible in our world. Finally I discuss how a given (and long) time record can be shown in an objective way to record an irreversible or reversible process. Or: can a direction of time be derived from its analysis? This leads quite naturally to examine if there is a possible spontaneous breaking of the time reversal symmetry in many body systems, a symmetry breaking that would be put in evidence objectively by looking at certain specific time correlations.
DEFF Research Database (Denmark)
Yuri, Shtarkov; Justesen, Jørn
1997-01-01
The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions.......The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions....
Directory of Open Access Journals (Sweden)
F. TopsÃƒÂ¸e
2001-09-01
Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over
International Nuclear Information System (INIS)
Ponman, T.J.
1984-01-01
For some years now two different expressions have been in use for maximum entropy image restoration and there has been some controversy over which one is appropriate for a given problem. Here two further entropies are presented and it is argued that there is no single correct algorithm. The properties of the four different methods are compared using simple 1D simulations with a view to showing how they can be used together to gain as much information as possible about the original object. (orig.)
Entanglement entropy and duality
Energy Technology Data Exchange (ETDEWEB)
Radičević, Ðorđe [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305-4060 (United States)
2016-11-22
Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors. We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.
Mathematical models and equilibrium in irreversible microeconomics
Directory of Open Access Journals (Sweden)
Anatoly M. Tsirlin
2010-07-01
Full Text Available A set of equilibrium states in a system consisting of economic agents, economic reservoirs, and firms is considered. Methods of irreversible microeconomics are used. We show that direct sale/purchase leads to an equilibrium state which depends upon the coefficients of supply/demand functions. To reach the unique equilibrium state it is necessary to add either monetary exchange or an intermediate firm.
Lattice-Valued Possibilistic Entropy Measure
Czech Academy of Sciences Publication Activity Database
Kramosil, Ivan
2008-01-01
Roč. 16, č. 6 (2008), s. 829-846 ISSN 0218-4885 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : complete lattice * lattice-valued possibilistic distribution * entropy measure * product of possibilistic distribution Subject RIV: BA - General Mathematics Impact factor: 1.000, year: 2008
Algebraic entropy for algebraic maps
International Nuclear Information System (INIS)
Hone, A N W; Ragnisco, Orlando; Zullo, Federico
2016-01-01
We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)
Revisiting entanglement entropy of lattice gauge theories
Energy Technology Data Exchange (ETDEWEB)
Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Lu, Shanghai 200433 (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University,220 Handan Lu, Shanghai 200433 (China); Wan, Yidun [Perimeter Institute for Theoretical Physics,31 Caroline Street, Waterloo, ON N2L 2Y5 (Canada)
2015-04-22
It is realized recently that the entanglement entropy in gauge theories is ambiguous because the Hilbert space cannot be expressed as a simple direct product of Hilbert spaces defined on the two regions; different ways of dividing the Hilbert spaces near the boundary leads to significantly different result, to the extreme that it could annihilate the otherwise finite topological entanglement entropy between two regions altogether. In this article, we first show that the topological entanglement entropy in the Kitaev model http://dx.doi.org/10.1016/S0003-4916(02)00018-0 which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiment, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.
International Nuclear Information System (INIS)
Hansen, Frank
2016-01-01
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.
Energy Technology Data Exchange (ETDEWEB)
Hansen, Frank, E-mail: frank.hansen@m.tohoku.ac.jp [Tohoku University, Institute for Excellence in Higher Education (Japan)
2016-06-15
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.
Relations Among Some Fuzzy Entropy Formulae
Institute of Scientific and Technical Information of China (English)
卿铭
2004-01-01
Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034 ...
Indian Academy of Sciences (India)
Consider the integral. taken over a reversible transformation. We shall call this function the entropy of state A.” 'Thermodynamics' by Enrico Fermi. “Let Γ be the volume of the region of motion of the states, and. This is the basic assumption of ...
Aur, Dorian; Vila-Rodriguez, Fidel
2017-01-01
Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy. The applied technique may offer new approaches to better understand nonlinear brain activity. Copyright Â© 2016 Elsevier B.V. All rights reserved.
Rescaling Temperature and Entropy
Olmsted, John, III
2010-01-01
Temperature and entropy traditionally are expressed in units of kelvin and joule/kelvin. These units obscure some important aspects of the natures of these thermodynamic quantities. Defining a rescaled temperature using the Boltzmann constant, T' = k[subscript B]T, expresses temperature in energy units, thereby emphasizing the close relationship…
Optimized Kernel Entropy Components.
Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau
2017-06-01
This brief addresses two main issues of the standard kernel entropy component analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of variance, as in the kernel principal components analysis. In this brief, we propose an extension of the KECA method, named optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular, it is based on the independent component analysis framework, and introduces an extra rotation to the eigen decomposition, which is optimized via gradient-ascent search. This maximum entropy preservation suggests that OKECA features are more efficient than KECA features for density estimation. In addition, a critical issue in both the methods is the selection of the kernel parameter, since it critically affects the resulting performance. Here, we analyze the most common kernel length-scale selection criteria. The results of both the methods are illustrated in different synthetic and real problems. Results show that OKECA returns projections with more expressive power than KECA, the most successful rule for estimating the kernel parameter is based on maximum likelihood, and OKECA is more robust to the selection of the length-scale parameter in kernel density estimation.
Zucker, M. H.
This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Vasile Patrascu
2017-01-01
This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Vasile Patrascu
2017-01-01
This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.
Entropy, information and Maxwell's demon after quantum mechanics
International Nuclear Information System (INIS)
Bhandari, Rajendra
1976-01-01
The problem of the subjective nature of entropy and its relation to information and irreversibility is examined in the light of the quantum measurement problem. The main thesis of the paper is that state collapse during a measurement and hence increase in the observed universe is seen by observers who are only able to observe a restricted manifold of states determined by their concepts, language, etc., in short by their level of perception. The thesis leads to the assertion that any universe with a structure must evolve. (author)
Reshaping the Science of Reliability with the Entropy Function
Directory of Open Access Journals (Sweden)
Paolo Rocchi
2015-01-01
Full Text Available The present paper revolves around two argument points. As first, we have observed a certain parallel between the reliability of systems and the progressive disorder of thermodynamical systems; and we import the notion of reversibility/irreversibility into the reliability domain. As second, we note that the reliability theory is a very active area of research which although has not yet become a mature discipline. This is due to the majority of researchers who adopt the inductive logic instead of the deductive logic typical of mature scientific sectors. The deductive approach was inaugurated by Gnedenko in the reliability domain. We mean to continue Gnedenko’s work and we use the Boltzmann-like entropy to pursue this objective. This paper condenses the papers published in the past decade which illustrate the calculus of the Boltzmann-like entropy. It is demonstrated how the every result complies with the deductive logic and are consistent with Gnedenko’s achievements.
Determination of LEDs degradation with entropy generation rate
Cuadras, Angel; Yao, Jiaqiang; Quilez, Marcos
2017-10-01
We propose a method to assess the degradation and aging of light emitting diodes (LEDs) based on irreversible entropy generation rate. We degraded several LEDs and monitored their entropy generation rate ( S ˙ ) in accelerated tests. We compared the thermoelectrical results with the optical light emission evolution during degradation. We find a good relationship between aging and S ˙ (t), because S ˙ is both related to device parameters and optical performance. We propose a threshold of S ˙ (t) as a reliable damage indicator of LED end-of-life that can avoid the need to perform optical measurements to assess optical aging. The method lays beyond the typical statistical laws for lifetime prediction provided by manufacturers. We tested different LED colors and electrical stresses to validate the electrical LED model and we analyzed the degradation mechanisms of the devices.
Evanescent magnetic field effects on entropy generation at the onset ...
Indian Academy of Sciences (India)
application of evanescent magnetic field not only suppresses the fluctuation of the ..... the Prigogine's theorem of minimum entropy production is unproven. ... consists in a double spiral configuration and viscous boundary layers in close ...
Statistical mechanics out of equilibrium the irreversibility
International Nuclear Information System (INIS)
Alvarez Estrada, R. F.
2001-01-01
A Round Table about the issue of Irreversibility and related matters has taken place during the last (20th) Statistical Mechanics Conference, held in Paris (July 1998). This article tries to provide a view (necessarily limited, and hence, uncompleted) of some approaches to the subject: the one based upon deterministic chaos (which is currently giving rise to a very active research) and the classical interpretation due to Boltzmann. An attempt has been made to write this article in a self-contained way, and to avoid a technical presentation wherever possible. (Author) 29 refs
Force-Time Entropy of Isometric Impulse.
Hsieh, Tsung-Yu; Newell, Karl M
2016-01-01
The relation between force and temporal variability in discrete impulse production has been viewed as independent (R. A. Schmidt, H. Zelaznik, B. Hawkins, J. S. Frank, & J. T. Quinn, 1979 ) or dependent on the rate of force (L. G. Carlton & K. M. Newell, 1993 ). Two experiments in an isometric single finger force task investigated the joint force-time entropy with (a) fixed time to peak force and different percentages of force level and (b) fixed percentage of force level and different times to peak force. The results showed that the peak force variability increased either with the increment of force level or through a shorter time to peak force that also reduced timing error variability. The peak force entropy and entropy of time to peak force increased on the respective dimension as the parameter conditions approached either maximum force or a minimum rate of force production. The findings show that force error and timing error are dependent but complementary when considered in the same framework with the joint force-time entropy at a minimum in the middle parameter range of discrete impulse.
Voter model with arbitrary degree dependence: clout, confidence and irreversibility
Fotouhi, Babak; Rabbat, Michael G.
2014-03-01
The voter model is widely used to model opinion dynamics in society. In this paper, we propose three modifications to incorporate heterogeneity into the model. We address the corresponding oversimplifications of the conventional voter model which are unrealistic. We first consider the voter model with popularity bias. The influence of each node on its neighbors depends on its degree. We find the consensus probabilities and expected consensus times for each of the states. We also find the fixation probability, which is the probability that a single node whose state differs from every other node imposes its state on the entire system. In addition, we find the expected fixation time. Then two other extensions to the model are proposed and the motivations behind them are discussed. The first one is confidence, where in addition to the states of neighbors, nodes take their own state into account at each update. We repeat the calculations for the augmented model and investigate the effects of adding confidence to the model. The second proposed extension is irreversibility, where one of the states is given the property that once nodes adopt it, they cannot switch back. This is motivated by applications where, agents take an irreversible action such as seeing a movie, purchasing a music album online, or buying a new product. The dynamics of densities, fixation times and consensus times are obtained.
Holographic Entanglement Entropy
Rangamani, Mukund
2016-01-01
We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to the concept of entanglement entropy in quantum field theories, review the holographic proposals for computing the same, providing some justification for where these proposals arise from in the first two parts. The final part addresses recent developments linking entanglement and geometry. We provide an overview of the various arguments and technical developments that teach us how to use field theory entanglement to detect geometry. Our discussion is by design eclectic; we have chosen to focus on developments that appear to us most promising for further insights into the holographic map. This is a preliminary draft of a few chapters of a book which will appear sometime in the near future, to be published by Springer. The book in addition contains a discussion of application o...
Entropy region and convolution
Czech Academy of Sciences Publication Activity Database
Matúš, František; Csirmaz, L.
2016-01-01
Roč. 62, č. 11 (2016), s. 6007-6018 ISSN 0018-9448 R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : entropy region * information-theoretic inequality * polymatroid Subject RIV: BD - Theory of Information Impact factor: 2.679, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/matus-0465564.pdf
Hyperspherical entanglement entropy
International Nuclear Information System (INIS)
Dowker, J S
2010-01-01
The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.
Hyperspherical entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Dowker, J S, E-mail: dowker@man.ac.u [Theory Group, School of Physics and Astronomy, University of Manchester, Manchester (United Kingdom)
2010-11-05
The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat spacetime is shown to equal the conformal anomaly by conformally transforming Euclideanized spacetime to a sphere and using already existing formulae for the relevant heat-kernel coefficients after cyclic factoring. The result follows from the fact that the conformal anomaly on this lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.
Entropy for Mechanically Vibrating Systems
Tufano, Dante
The research contained within this thesis deals with the subject of entropy as defined for and applied to mechanically vibrating systems. This work begins with an overview of entropy as it is understood in the fields of classical thermodynamics, information theory, statistical mechanics, and statistical vibroacoustics. Khinchin's definition of entropy, which is the primary definition used for the work contained in this thesis, is introduced in the context of vibroacoustic systems. The main goal of this research is to to establish a mathematical framework for the application of Khinchin's entropy in the field of statistical vibroacoustics by examining the entropy context of mechanically vibrating systems. The introduction of this thesis provides an overview of statistical energy analysis (SEA), a modeling approach to vibroacoustics that motivates this work on entropy. The objective of this thesis is given, and followed by a discussion of the intellectual merit of this work as well as a literature review of relevant material. Following the introduction, an entropy analysis of systems of coupled oscillators is performed utilizing Khinchin's definition of entropy. This analysis develops upon the mathematical theory relating to mixing entropy, which is generated by the coupling of vibroacoustic systems. The mixing entropy is shown to provide insight into the qualitative behavior of such systems. Additionally, it is shown that the entropy inequality property of Khinchin's entropy can be reduced to an equality using the mixing entropy concept. This equality can be interpreted as a facet of the second law of thermodynamics for vibroacoustic systems. Following this analysis, an investigation of continuous systems is performed using Khinchin's entropy. It is shown that entropy analyses using Khinchin's entropy are valid for continuous systems that can be decomposed into a finite number of modes. The results are shown to be analogous to those obtained for simple oscillators
Irreversible electroporation: state of the art
Directory of Open Access Journals (Sweden)
Wagstaff PGK
2016-04-01
Full Text Available Peter GK Wagstaff,1 Mara Buijs,1 Willemien van den Bos,1 Daniel M de Bruin,2 Patricia J Zondervan,1 Jean JMCH de la Rosette,1 M Pilar Laguna Pes1 1Department of Urology, 2Department of Biomedical Engineering and Physics, Academic Medical Center, Amsterdam, the Netherlands Abstract: The field of focal ablative therapy for the treatment of cancer is characterized by abundance of thermal ablative techniques that provide a minimally invasive treatment option in selected tumors. However, the unselective destruction inflicted by thermal ablation modalities can result in damage to vital structures in the vicinity of the tumor. Furthermore, the efficacy of thermal ablation intensity can be impaired due to thermal sink caused by large blood vessels in the proximity of the tumor. Irreversible electroporation (IRE is a novel ablation modality based on the principle of electroporation or electropermeabilization, in which electric pulses are used to create nanoscale defects in the cell membrane. In theory, IRE has the potential of overcoming the aforementioned limitations of thermal ablation techniques. This review provides a description of the principle of IRE, combined with an overview of in vivo research performed to date in the liver, pancreas, kidney, and prostate. Keywords: irreversible electroporation, IRE, tumor, ablation, focal therapy, cancer
Preimage entropy dimension of topological dynamical systems
Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao
2014-01-01
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...
Caticha, Ariel
2007-11-01
What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.
Directory of Open Access Journals (Sweden)
Bernard S. Kay
2015-12-01
Full Text Available We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS/conformal field theory (CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.
Irreversible thermodynamics of overdriven shocks in solids
International Nuclear Information System (INIS)
Wallace, D.C.
1981-01-01
An isotropic solid capable of transporting heat and of undergoing dissipative plastic flow, is treated. The shock is assumed to be a steady wave, and any phase changes or macroscopic inhomogeneities which might be induced by the shock are neglected. Under these conditions it is established that for an overdriven shock, no solution is possible without heat transport, and when the heat transport is governed by the steady conduction equation, no solution is possible without plastic dissipation as well. Upper and lower bounds are established for the thermodynamic variables, namely the shear stress, temperature, entropy, plastic strain, and heat flux, as functions of compression through the shock
Entanglement entropy and differential entropy for massive flavors
International Nuclear Information System (INIS)
Jones, Peter A.R.; Taylor, Marika
2015-01-01
In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.
The Value of Fighting Irreversible Demise by Softening the Irreversible Cost
Magis, P.; Sbuelz, A.
2005-01-01
We study a novel issue in the real-options-based technology innovation literature by means of double barrier contingent claims analysis.We show how much a ¯rm with the monopoly over a project is willing to spend in investment technology innovation that softens the irreversible cost of accessing the
Goyal, Megha; Chaudhuri, Tapan K; Kuwajima, Kunihiro
2014-01-01
Thermal denaturation of Escherichia coli maltodextrin glucosidase was studied by differential scanning calorimetry, circular dichroism (230 nm), and UV-absorption measurements (340 nm), which were respectively used to monitor heat absorption, conformational unfolding, and the production of solution turbidity. The denaturation was irreversible, and the thermal transition recorded at scan rates of 0.5-1.5 K/min was significantly scan-rate dependent, indicating that the thermal denaturation was kinetically controlled. The absence of a protein-concentration effect on the thermal transition indicated that the denaturation was rate-limited by a mono-molecular process. From the analysis of the calorimetric thermograms, a one-step irreversible model well represented the thermal denaturation of the protein. The calorimetrically observed thermal transitions showed excellent coincidence with the turbidity transitions monitored by UV-absorption as well as with the unfolding transitions monitored by circular dichroism. The thermal denaturation of the protein was thus rate-limited by conformational unfolding, which was followed by a rapid irreversible formation of aggregates that produced the solution turbidity. It is thus important to note that the absence of the protein-concentration effect on the irreversible thermal denaturation does not necessarily means the absence of protein aggregation itself. The turbidity measurements together with differential scanning calorimetry in the irreversible thermal denaturation of the protein provided a very effective approach for understanding the mechanisms of the irreversible denaturation. The Arrhenius-equation parameters obtained from analysis of the thermal denaturation were compared with those of other proteins that have been reported to show the one-step irreversible thermal denaturation. Maltodextrin glucosidase had sufficiently high kinetic stability with a half-life of 68 days at a physiological temperature (37°C).
Directory of Open Access Journals (Sweden)
Daniele Penteado Rosa
2013-02-01
Full Text Available Orange seeds are a promising agroindustry-waste which can be implemented in the extraction and production of vegetable oil. The relationship between moisture content and water activity provides useful information for the processing and storage of this waste item. The aim of this study was to determine the mechanism of water sorption enthalpy-entropy of orange seeds (C. sinensis cv. Brazilians according to the moisture content. Therefore, desorption isotherms were determined at five different temperature (30, 40, 50, 60, and 70 ºC under a wide range of moisture content (0.005-0.057 kg kg-1 d.b. and water activity (0.02-0.756. Theoretical and empirical models were used for modeling the desorption isotherms. An analytical solution of the Clausius-Clapeyron equation was proposed to compute the isosteric heat of sorption, the differential entropy, and Gibbs free energy using the Oswin model when the effect of temperature on the hygroscopic equilibrium was considered.
Large Eddy Simulation of Entropy Generation in a Turbulent Mixing Layer
Sheikhi, Reza H.; Safari, Mehdi; Hadi, Fatemeh
2013-11-01
Entropy transport equation is considered in large eddy simulation (LES) of turbulent flows. The irreversible entropy generation in this equation provides a more general description of subgrid scale (SGS) dissipation due to heat conduction, mass diffusion and viscosity effects. A new methodology is developed, termed the entropy filtered density function (En-FDF), to account for all individual entropy generation effects in turbulent flows. The En-FDF represents the joint probability density function of entropy, frequency, velocity and scalar fields within the SGS. An exact transport equation is developed for the En-FDF, which is modeled by a system of stochastic differential equations, incorporating the second law of thermodynamics. The modeled En-FDF transport equation is solved by a Lagrangian Monte Carlo method. The methodology is employed to simulate a turbulent mixing layer involving transport of passive scalars and entropy. Various modes of entropy generation are obtained from the En-FDF and analyzed. Predictions are assessed against data generated by direct numerical simulation (DNS). The En-FDF predictions are in good agreements with the DNS data.
Logarithmic black hole entropy corrections and holographic Renyi entropy
Energy Technology Data Exchange (ETDEWEB)
Mahapatra, Subhash [The Institute of Mathematical Sciences, Chennai (India); KU Leuven - KULAK, Department of Physics, Kortrijk (Belgium)
2018-01-15
The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G{sub D}{sup 0}. The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy
Directory of Open Access Journals (Sweden)
Maya Gupta
2010-04-01
Full Text Available Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.
Logarithmic black hole entropy corrections and holographic Renyi entropy
International Nuclear Information System (INIS)
Mahapatra, Subhash
2018-01-01
The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)
Suprono, Montry S; Kattadiyil, Mathew T; Goodacre, Charles J; Winer, Myron S
2012-10-01
Many new products have been introduced and marketed as alternatives to traditional irreversible hydrocolloid materials. These alternative materials have the same structural formula as addition reaction silicone, also known as vinyl polysiloxane (VPS), impression materials. Currently, there is limited in vitro and in vivo research on these products, including on the effects of chemical disinfectants on the materials. The purpose of this study was to compare the effects of a spray disinfecting technique on a traditional irreversible hydrocolloid and 3 new alternative impression materials in vitro. The tests were performed in accordance with the American National Standards Institute/American Dental Association (ANSI/ADA) Specification Nos. 18 and 19. Under standardized conditions, 100 impressions were made of a ruled test block with an irreversible hydrocolloid and 3 alternative impression materials. Nondisinfected irreversible hydrocolloid was used as the control. The impressions were examined for surface detail reproduction before and after disinfection with a chloramine-T product. Type III and Type V dental stone casts were evaluated for linear dimensional change and gypsum compatibility. Comparisons of linear dimensional change were analyzed with 2-way ANOVA of mean ranks with the Scheffé post hoc comparisons (α=.05). Data for surface detail reproduction were analyzed with the Wilcoxon Signed-Rank procedure and gypsum compatibility with the Kruskal-Wallis Rank procedure (α=.05). The alternative impression materials demonstrated significantly better outcomes with all 3 parameters tested. Disinfection with chloroamine-T did not have any effect on the 3 alternative impression materials. The irreversible hydrocolloid groups produced the most variability in the measurements of linear dimensional change. All of the tested materials were within the ADA's acceptable limit of 1.0% for linear dimensional change, except for the disinfected irreversible hydrocolloid
Anistropically varying conductivity in irreversible electroporation simulations.
Labarbera, Nicholas; Drapaca, Corina
2017-11-01
One recent area of cancer research is irreversible electroporation (IRE). Irreversible electroporation is a minimally invasive procedure where needle electrodes are inserted into the body to ablate tumor cells with electricity. The aim of this paper is to propose a mathematical model that incorporates a tissue's conductivity increasing more in the direction of the electrical field as this has been shown to occur in experiments. It was necessary to mathematically derive a valid form of the conductivity tensor such that it is dependent on the electrical field direction and can be easily implemented into numerical software. The derivation of a conductivity tensor that can take arbitrary functions for the conductivity in the directions tangent and normal to the electrical field is the main contribution of this paper. Numerical simulations were performed for isotropic-varying and anisotropic-varying conductivities to evaluate the importance of including the electrical field's direction in the formulation for conductivity. By starting from previously published experimental results, this paper derived a general formulation for an anistropic-varying tensor for implementation into irreversible electroporation modeling software. The anistropic-varying tensor formulation allows the conductivity to take into consideration both electrical field direction and magnitude, as opposed to previous published works that only took into account electrical field magnitude. The anisotropic formulation predicts roughly a five percent decrease in ablation size for the monopolar simulation and approximately a ten percent decrease in ablation size for the bipolar simulations. This is a positive result as previously reported results found the isotropic formulation to overpredict ablation size for both monopolar and bipolar simulations. Furthermore, it was also reported that the isotropic formulation overpredicts the ablation size more for the bipolar case than the monopolar case. Thus, our
Entropy: From Thermodynamics to Hydrology
Directory of Open Access Journals (Sweden)
Demetris Koutsoyiannis
2014-02-01
Full Text Available Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.
Credal Networks under Maximum Entropy
Lukasiewicz, Thomas
2013-01-01
We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. ...
Basic quantum irreversibility in neutron interferometry
International Nuclear Information System (INIS)
Rauch, H
2009-01-01
The transition between the quantum and classical world is a topical problem in quantum physics, which can be investigated by neutron interferometric methods. Here we discuss unavoidable quantum losses as they appear in neutron phase-echo and spin rotation experiments and we show how entanglement effects in a single-particle system demonstrate quantum contextuality, i.e. an entanglement between external and internal degrees of freedom in single-particle systems. This contextuality phenomenon also shows that a quantum system carries much more information than usually extracted. In all cases of an interaction, parasitic beams are produced which cannot be recombined completely with the original beam. This means that a complete reconstruction of the original state is, in principle, impossible which causes a kind of intrinsic irreversibility. Even small interaction potentials can have huge effects when they are applied in quantum Zeno-like experiments. The path towards advanced neutron quantum optics will be discussed.
Competing irreversible cooperative reactions on polymer chains
International Nuclear Information System (INIS)
Evans, J.W.; Hoffman, D.K.; Burgess, D.R.
1984-01-01
We analyze model processes involving competition between several irreversible reactions at the sites of a 1D, infinite, uniform polymer chain. These reactions can be cooperative, i.e., the corresponding rates depend on the state of the surrounding sites. An infinite hierarchy of rate equations is readily derived for the probabilities of various subconfigurations. By exploiting a shielding property of suitable blocks of unreacted sites, we show how exact hierarchy truncation and solution is sometimes possible. The behavior of solutions is illustrated in several cases by plotting families of ''reaction trajectories'' for varying ratios of reactant concentrations. As a specific application, we consider competition between coordination of ZnCl 2 to pairs of oxygen atoms and to single oxygen atoms in poly(propylene oxide). The observed glass transition temperature behavior is eludicated
Synergetcs - a field beyond irreversible thermodynamics
International Nuclear Information System (INIS)
Haken, H.
1978-01-01
This lecture introduces the reader to synergetics, a very young field of interdisciplinary research, which is devoted to the question of self-organization and, quite generally, to the birth of new qualities. After comparing the role of thermodynamics, irreversible thermodynamics and synergetics in the description of phenomena we give a few examples for self-oragnizing systems. Next we outline the mathematical approach and consider the generalized Ginzburg-Landau equations for non equilibrium phase transitions. We continue by applying these equations to the problem of morphogenesis in biology. We close our lecture by extending the formalism to spatially inhomogeneous or oscillating systems and arrive at order-parameter equations which are capable of describing new large classes of higher bifurcation schemes. (HJ)
Chemical kinetics, stochastic processes, and irreversible thermodynamics
Santillán, Moisés
2014-01-01
This book brings theories in nonlinear dynamics, stochastic processes, irreversible thermodynamics, physical chemistry, and biochemistry together in an introductory but formal and comprehensive manner. Coupled with examples, the theories are developed stepwise, starting with the simplest concepts and building upon them into a more general framework. Furthermore, each new mathematical derivation is immediately applied to one or more biological systems. The last chapters focus on applying mathematical and physical techniques to study systems such as: gene regulatory networks and ion channels. The target audience of this book are mainly final year undergraduate and graduate students with a solid mathematical background (physicists, mathematicians, and engineers), as well as with basic notions of biochemistry and cellular biology. This book can also be useful to students with a biological background who are interested in mathematical modeling, and have a working knowledge of calculus, differential equatio...
Editorial: Entropy in Landscape Ecology
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Samuel A. Cushman
2018-04-01
Full Text Available Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.
Entropy and transverse section reconstruction
International Nuclear Information System (INIS)
Gullberg, G.T.
1976-01-01
A new approach to the reconstruction of a transverse section using projection data from multiple views incorporates the concept of maximum entropy. The principle of maximizing information entropy embodies the assurance of minimizing bias or prejudice in the reconstruction. Using maximum entropy is a necessary condition for the reconstructed image. This entropy criterion is most appropriate for 3-D reconstruction of objects from projections where the system is underdetermined or the data are limited statistically. This is the case in nuclear medicine time limitations in patient studies do not yield sufficient projections
Directory of Open Access Journals (Sweden)
A.S. Eegunjobi
Full Text Available Numerical analysis of the intrinsic irreversibility of a mixed convection hydromagnetic flow of an electrically conducting couple stress fluid through upright channel filled with a saturated porous medium and radiative heat transfer was carried out. The thermodynamics first and second laws were employed to examine the problem. We obtained the dimensionless nonlinear differential equations and solves numerically with shooting procedure joined with a fourth order Runge-Kutta-Fehlberg integration scheme. The temperature and velocity obtained, used to analyse the entropy generation rate together with some various physical parameters of the flow. Our results are presented graphically and talk over. Keywords: MHD channel flow, Couple stress fluid, Porous medium, Thermal radiation, Entropy generation, Injection/suction
Entropy Generation Minimization for Reverse Water Gas Shift (RWGS Reactors
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Lei Zhang
2018-05-01
Full Text Available Thermal design and optimization for reverse water gas shift (RWGS reactors is particularly important to fuel synthesis in naval or commercial scenarios. The RWGS reactor with irreversibilities of heat transfer, chemical reaction and viscous flow is studied based on finite time thermodynamics or entropy generation minimization theory in this paper. The total entropy generation rate (EGR in the RWGS reactor with different boundary conditions is minimized subject to specific feed compositions and chemical conversion using optimal control theory, and the optimal configurations obtained are compared with three reference reactors with linear, constant reservoir temperature and constant heat flux operations, which are commonly used in engineering. The results show that a drastic EGR reduction of up to 23% can be achieved by optimizing the reservoir temperature profile, the inlet temperature of feed gas and the reactor length simultaneously, compared to that of the reference reactor with the linear reservoir temperature. These optimization efforts are mainly achieved by reducing the irreversibility of heat transfer. Optimal paths have subsections of relatively constant thermal force, chemical force and local EGR. A conceptual optimal design of sandwich structure for the compact modular reactor is proposed, without elaborate control tools or excessive interstage equipment. The results can provide guidelines for designing industrial RWGS reactors in naval or commercial scenarios.
Nonextensive entropy interdisciplinary applications
Tsallis, Constantino
2004-01-01
A great variety of complex phenomena in many scientific fields exhibit power-law behavior, reflecting a hierarchical or fractal structure. Many of these phenomena seem to be susceptible to description using approaches drawn from thermodynamics or statistical mechanics, particularly approaches involving the maximization of entropy and of Boltzmann-Gibbs statistical mechanics and standard laws in a natural way. The book addresses the interdisciplinary applications of these ideas, and also on various phenomena that could possibly be quantitatively describable in terms of these ideas.
Minimum Error Entropy Classification
Marques de Sá, Joaquim P; Santos, Jorge M F; Alexandre, Luís A
2013-01-01
This book explains the minimum error entropy (MEE) concept applied to data classification machines. Theoretical results on the inner workings of the MEE concept, in its application to solving a variety of classification problems, are presented in the wider realm of risk functionals. Researchers and practitioners also find in the book a detailed presentation of practical data classifiers using MEE. These include multi‐layer perceptrons, recurrent neural networks, complexvalued neural networks, modular neural networks, and decision trees. A clustering algorithm using a MEE‐like concept is also presented. Examples, tests, evaluation experiments and comparison with similar machines using classic approaches, complement the descriptions.
Information Entropy Measures for Stand Structural Diversity:Joint Entropy
Institute of Scientific and Technical Information of China (English)
Lei Xiangdong; Lu Yuanchang
2004-01-01
Structural diversity is the key attribute of a stand. A set of biodiversity measures in ecology was introduced in forest management for describing stand structure, of which Shannon information entropy (Shannon index) has been the most widely used measure of species diversity. It is generally thought that tree size diversity could serve as a good proxy for height diversity. However, tree size diversity and height diversity for stand structure is not completely consistent. Stand diameter cannot reflect height information completely. Either tree size diversity or height diversity is one-dimensional information entropy measure. This paper discussed the method of multiple-dimensional information entropy measure with the concept of joint entropy. It is suggested that joint entropy is a good measure for describing overall stand structural diversity.
Weak entropy inequalities and entropic convergence
Institute of Scientific and Technical Information of China (English)
2008-01-01
A criterion for algebraic convergence of the entropy is presented and an algebraic convergence result for the entropy of an exclusion process is improved. A weak entropy inequality is considered and its relationship to entropic convergence is discussed.
Entropy concentration and the empirical coding game
Grünwald, P.D.
2008-01-01
We give a characterization of maximum entropy/minimum relative entropy inference by providing two 'strong entropy concentration' theorems. These theorems unify and generalize Jaynes''concentration phenomenon' and Van Campenhout and Cover's 'conditional limit theorem'. The theorems characterize
Crossing the entropy barrier of dynamical zeta functions
International Nuclear Information System (INIS)
Aurich, R.; Bolte, J.; Matthies, C.; Sieber, M.; Steiner, F.
1992-01-01
Dynamical zeta functions are an important tool to quantize chaotic dynamical systems. The basic quantization rules require the computation of the zeta functions on the real energy axis, where the Euler product representations running over the classical periodic orbits usually do not converge due to the existence of the so-called entropy barrier determined by the topological entropy of the classical system. We shown that the convergence properties of the dynamical zeta functions rewritten as Dirichlet series are governed not only by the well-known topological and metric entropy, but depend crucially on subtle statistical properties of the Maslow indices and of the multiplicities of the periodic orbits that are measured by a new parameter for which we introduce the notion of a third entropy. If and only if the third entropy is nonvanishing, one can cross the entropy barrier; if it exceeds a certain value, one can even compute the zeta function in the physical region by means of a convergent Dirichlet series. A simple statistical model is presented which allows to compute the third entropy. Four examples of chaotic systems are studied in detail to test the model numerically. (orig.)
Crossing the entropy barrier of dynamical zeta functions
Energy Technology Data Exchange (ETDEWEB)
Aurich, R.; Bolte, J.; Matthies, C.; Sieber, M.; Steiner, F. (Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik)
1992-01-01
Dynamical zeta functions are an important tool to quantize chaotic dynamical systems. The basic quantization rules require the computation of the zeta functions on the real energy axis, where the Euler product representations running over the classical periodic orbits usually do not converge due to the existence of the so-called entropy barrier determined by the topological entropy of the classical system. We shown that the convergence properties of the dynamical zeta functions rewritten as Dirichlet series are governed not only by the well-known topological and metric entropy, but depend crucially on subtle statistical properties of the Maslow indices and of the multiplicities of the periodic orbits that are measured by a new parameter for which we introduce the notion of a third entropy. If and only if the third entropy is nonvanishing, one can cross the entropy barrier; if it exceeds a certain value, one can even compute the zeta function in the physical region by means of a convergent Dirichlet series. A simple statistical model is presented which allows to compute the third entropy. Four examples of chaotic systems are studied in detail to test the model numerically. (orig.).
Directory of Open Access Journals (Sweden)
John Scales Avery
2012-04-01
Full Text Available In this essay, human society is regarded as a “superorganism”, analogous to colonies of social insects. The digestive system of the human superorganism is the global economy, which ingests both free energy and resources, and later excretes them in a degraded form. This process involves an increase in entropy. Early in the 20th century, both Frederick Soddy and Nicholas Georgescu-Roegen discussed the relationship between entropy and economics. Soddy called for an index system to regulate the money supply and a reform of the fractional reserve banking system, while Georgescu-Roegen pointed to the need for Ecological Economics, a steady-state economy, and population stabilization. As we reach the end of the fossil fuel era and as industrial growth falters, massive unemployment can only be avoided by responsible governmental action. The necessary steps include shifting labor to projects needed for a sustainable economy, dividing the available work fairly among those seeking employment, and reforming the practices of the financial sector.
International Nuclear Information System (INIS)
Steinmeyer, D.
1992-01-01
When we talk about saving energy what we usually mean is not wasting work. What we try to do when we design a process, is to use work as effectively as possible. It's hard to do that if we can't see it clearly. This paper illustrates how work can be seen (or calculated) without imposing entropy as a screen in front of it. We've all heard that the second law tells us that the entropy of the universe is increasing, and we are left with the feeling that the universe is ultimately headed for chaos, but receive little other information from this statement. A slightly more useful statement of the second law is the work potential of the universe is decreasing. However, this statement carries a needlessly negative ring. A simplified definition of the second law is: It takes work to change things. With these two corollaries: We can calculate the theoretical minimum work needed for a given change; and We can express the value of all changes in terms of work
On the entropy of a hidden Markov process.
Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech
2008-05-01
We study the entropy rate of a hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a first-order binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By presenting the probability of a sequence under the model as a product of random matrices, one can see that the entropy rate sought is equal to a top Lyapunov exponent of the product. This offers an explanation for the elusiveness of explicit expressions for the HMP entropy rate, as Lyapunov exponents are notoriously difficult to compute. Consequently, we focus on asymptotic estimates, and apply the same product of random matrices to derive an explicit expression for a Taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel. The accuracy of the approximation is validated against empirical simulation results. We also extend our results to higher-order Markov processes and to Rényi entropies of any order.
Possible extended forms of thermodynamic entropy
International Nuclear Information System (INIS)
Sasa, Shin-ichi
2014-01-01
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon entropy of the microscopic degrees of freedom. Whenever an extension of thermodynamic entropy is attempted, we must pay special attention to how its three different aspects just mentioned are altered. In this paper, we discuss possible extensions of the thermodynamic entropy. (paper)
Configurational entropy of glueball states
Energy Technology Data Exchange (ETDEWEB)
Bernardini, Alex E., E-mail: alexeb@ufscar.br [Departamento de Física, Universidade Federal de São Carlos, PO Box 676, 13565-905, São Carlos, SP (Brazil); Braga, Nelson R.F., E-mail: braga@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [CMCC, Universidade Federal do ABC, UFABC, 09210-580, Santo André (Brazil)
2017-02-10
The configurational entropy of glueball states is calculated using a holographic description. Glueball states are represented by a supergravity dual picture, consisting of a 5-dimensional graviton–dilaton action of a dynamical holographic AdS/QCD model. The configurational entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.
Thermostatistical aspects of generalized entropies
International Nuclear Information System (INIS)
Fa, K.S.; Lenzi, E.K.
2004-01-01
We investigate the properties concerning a class of generalized entropies given by S q,r =k{1-[Σ i p i q ] r }/[r(q-1)] which include Tsallis' entropy (r=1), the usual Boltzmann-Gibbs entropy (q=1), Renyi's entropy (r=0) and normalized Tsallis' entropy (r=-1). In order to obtain the generalized thermodynamic relations we use the laws of thermodynamics and considering the hypothesis that the joint probability of two independent systems is given by p ij A c upB =p i A p j B . We show that the transmutation which occurs from Tsallis' entropy to Renyi's entropy also occur with S q,r . In this scenario, we also analyze the generalized variance, covariance and correlation coefficient of a non-interacting system by using extended optimal Lagrange multiplier approach. We show that the correlation coefficient tends to zero in the thermodynamic limit. However, Renyi's entropy related to this non-interacting system presents a certain degree of non-extensivity
Entropy statistics and information theory
Frenken, K.; Hanusch, H.; Pyka, A.
2007-01-01
Entropy measures provide important tools to indicate variety in distributions at particular moments in time (e.g., market shares) and to analyse evolutionary processes over time (e.g., technical change). Importantly, entropy statistics are suitable to decomposition analysis, which renders the
Black brane entropy and hydrodynamics
Booth, I.; Heller, M.P.; Spaliński, M.
2010-01-01
A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics
Black brane entropy and hydrodynamics
Booth, I.; Heller, M.P.; Spaliński, M.
2011-01-01
A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics
High Entropy Random Selection Protocols
H. Buhrman (Harry); M. Christandl (Matthias); M. Koucky (Michal); Z. Lotker (Zvi); B. Patt-Shamir; M. Charikar; K. Jansen; O. Reingold; J. Rolim
2007-01-01
textabstractIn this paper, we construct protocols for two parties that do not trust each other, to generate random variables with high Shannon entropy. We improve known bounds for the trade off between the number of rounds, length of communication and the entropy of the outcome.
Absolute entropy of ions in methanol
International Nuclear Information System (INIS)
Abakshin, V.A.; Kobenin, V.A.; Krestov, G.A.
1978-01-01
By measuring the initial thermoelectromotive forces of chains with bromo-silver electrodes in tetraalkylammonium bromide solutions the absolute entropy of bromide-ion in methanol is determined in the 298.15-318.15 K range. The anti Ssub(Brsup(-))sup(0) = 9.8 entropy units value is used for calculation of the absolute partial molar entropy of alkali metal ions and halogenide ions. It has been found that, absolute entropy of Cs + =12.0 entropy units, I - =14.0 entropy units. The obtained ion absolute entropies in methanol at 298.15 K within 1-2 entropy units is in an agreement with published data
Entropy and equilibrium via games of complexity
Topsøe, Flemming
2004-09-01
It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy ( q-entropy) and Kaniadakis entropy ( κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.
Entropy inequalities from reflection positivity
International Nuclear Information System (INIS)
Casini, H
2010-01-01
We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real-time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed
Entropy Budget for Hawking Evaporation
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Ana Alonso-Serrano
2017-07-01
Full Text Available Blackbody radiation, emitted from a furnace and described by a Planck spectrum, contains (on average an entropy of 3 . 9 ± 2 . 5 bits per photon. Since normal physical burning is a unitary process, this amount of entropy is compensated by the same amount of “hidden information” in correlations between the photons. The importance of this result lies in the posterior extension of this argument to the Hawking radiation from black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget for the evaporation process. In order to carry out this calculation, we adopt a variant of the “average subsystem” approach, but consider a tripartite pure system that includes the influence of the rest of the universe, and which allows “young” black holes to still have a non-zero entropy; which we identify with the standard Bekenstein entropy.
The Social Cost of Stochastic and Irreversible Climate Change
Cai, Y.; Judd, K. L.; Lontzek, T.
2013-12-01
Many scientists are worried about climate change triggering abrupt and irreversible events leading to significant and long-lasting damages. For example, a rapid release of methane from permafrost may lead to amplified global warming, and global warming may increase the frequency and severity of heavy rainfall or typhoon, destroying large cities and killing numerous people. Some elements of the climate system which might exhibit such a triggering effect are called tipping elements. There is great uncertainty about the impact of anthropogenic carbon and tipping elements on future economic wellbeing. Any rational policy choice must consider the great uncertainty about the magnitude and timing of global warming's impact on economic productivity. While the likelihood of tipping points may be a function of contemporaneous temperature, their effects are long lasting and might be independent of future temperatures. It is assumed that some of these tipping points might occur even in this century, but also that their duration and post-tipping impact are uncertain. A faithful representation of the possibility of tipping points for the calculation of social cost of carbon would require a fully stochastic formulation of irreversibility, and accounting for the deep layer of uncertainties regarding the duration of the tipping process and also its economic impact. We use DSICE, a DSGE extension of the DICE2007 model of William Nordhaus, which incorporates beliefs about the uncertain economic impact of possible climate tipping events and uses empirically plausible parameterizations of Epstein-Zin preferences to represent attitudes towards risk. We find that the uncertainty associated with anthropogenic climate change imply carbon taxes much higher than implied by deterministic models. This analysis indicates that the absence of uncertainty in DICE2007 and similar IAM models may result in substantial understatement of the potential benefits of policies to reduce GHG emissions.
International Nuclear Information System (INIS)
Xu, Zhichao; Guo, Juncheng; Lin, Guoxing; Chen, Jincan
2016-01-01
On the basis of the Langevin theory of classical statistical mechanics, the magnetization, entropy, and iso-field heat capacity of ferromagnetic materials are analyzed and their mathematical expressions are derived. An irreversible regenerative Ericsson refrigeration cycle by using a ferromagnetic material as the working substance is established, in which finite heat capacity rates of low and high temperature reservoirs, non-perfect regenerative heat of the refrigeration cycle, additional regenerative heat loss, etc. are taken into account. Based on the regenerative refrigeration cycle model, a thermoeconomic function is introduced as one objective function and optimized with respect to the temperatures of the working substance in the two iso-thermal processes. By means of numerical calculation, the effects of the effective factor of the heat exchangers in high/low temperature reservoir sides, efficiency of the regenerator, heat capacity rate of the low temperature reservoir, and applied magnetic field on the optimal thermoeconomic function as well as the corresponding cooling rate and coefficient of performance are revealed. The results obtained in this paper can provide some theoretical guidance for the optimal design of actual regenerative magnetic refrigerator cycle. - Highlights: • Thermodynamic performance of ferromagnetic material is analyzed. • An irreversible regenerative ferromagnetic Ericsson refrigeration cycle is set up. • The thermoeconomic objective function is introduced and optimized. • Impacts of the thermoeconomic and other parameters are discussed.
Time-dependent entropy evolution in microscopic and macroscopic electromagnetic relaxation
International Nuclear Information System (INIS)
Baker-Jarvis, James
2005-01-01
This paper is a study of entropy and its evolution in the time and frequency domains upon application of electromagnetic fields to materials. An understanding of entropy and its evolution in electromagnetic interactions bridges the boundaries between electromagnetism and thermodynamics. The approach used here is a Liouville-based statistical-mechanical theory. I show that the microscopic entropy is reversible and the macroscopic entropy satisfies an H theorem. The spectral entropy development can be very useful for studying the frequency response of materials. Using a projection-operator based nonequilibrium entropy, different equations are derived for the entropy and entropy production and are applied to the polarization, magnetization, and macroscopic fields. I begin by proving an exact H theorem for the entropy, progress to application of time-dependent entropy in electromagnetics, and then apply the theory to relevant applications in electromagnetics. The paper concludes with a discussion of the relationship of the frequency-domain form of the entropy to the permittivity, permeability, and impedance
Formation of Irreversible H-bonds in Cellulose Materials
Umesh P. Agarwal; Sally A. Ralph; Rick S. Reiner; Nicole M. Stark
2015-01-01
Understanding of formation of irreversible Hbonds in cellulose is important in a number of fields. For example, fields as diverse as pulp and paper and enzymatic saccharification of cellulose are affected. In the present investigation, the phenomenon of formation of irreversible H-bonds is studied in a variety of celluloses and under two different drying conditions....
Guinea pig ductus arteriosus. II - Irreversible closure after birth.
Fay, F. S.; Cooke, P. H.
1972-01-01
To investigate the mechanism underlying irreversibility of ductal closure after birth, studies were undertaken to determine the exact time course for the onset of irreversible closure of the guinea pig ductus arteriosus. Parallel studies of the reactivity of ductal smooth muscle to oxygen and studies of the postpartum cellular changes within the vessel were also carried out.
Transition to Clean Capital, Irreversible Investment and Stranded Assets
Rozenberg, Julie; Vogt-Schilb, Adrien; Hallegatte, Stephane
2014-01-01
This paper uses a Ramsey model with two types of capital to analyze the optimal transition to clean capital when polluting investment is irreversible. The cost of climate mitigation decomposes as a technical cost of using clean instead of polluting capital and a transition cost from the irreversibility of pre-existing polluting capital. With a carbon price, the transition cost can be limit...
Irreversible energy flow in forced Vlasov dynamics
Plunk, Gabriel G.
2014-10-01
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag. The recent paper of Plunk [G.G. Plunk, Phys. Plasmas 20, 032304 (2013)] considered the forced linear Vlasov equation as a model for the quasi-steady state of a single stable plasma wavenumber interacting with a bath of turbulent fluctuations. This approach gives some insight into possible energy flows without solving for nonlinear dynamics. The central result of the present work is that the forced linear Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all orders under a detuning of the forcing frequency and the characteristic frequency associated with particle streaming. We first prove this by direct calculation, tracking energy flow in terms of certain exact conservation laws of the linear (collisionless) Vlasov equation. Then we analyze the steady-state solutions in detail using a weakly collisional Hermite-moment formulation, and compare with numerical solution. This leads to a detailed description of the Hermite energy spectrum, and a proof of no dissipation at all orders, complementing the collisionless Vlasov result.
Irreversible energy flow in forced Vlasov dynamics
Plunk, Gabriel G.; Parker, Joseph T.
2014-01-01
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag. The recent paper of Plunk [G.G. Plunk, Phys. Plasmas 20, 032304 (2013)] considered the forced linear Vlasov equation as a model for the quasi-steady state of a single stable plasma wavenumber interacting with a bath of turbulent fluctuations. This approach gives some insight into possible energy flows without solving for nonlinear dynamics. The central result of the present work is that the forced linear Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all orders under a detuning of the forcing frequency and the characteristic frequency associated with particle streaming. We first prove this by direct calculation, tracking energy flow in terms of certain exact conservation laws of the linear (collisionless) Vlasov equation. Then we analyze the steady-state solutions in detail using a weakly collisional Hermite-moment formulation, and compare with numerical solution. This leads to a detailed description of the Hermite energy spectrum, and a proof of no dissipation at all orders, complementing the collisionless Vlasov result.
On the Spectral Entropy of Thermodynamic Paths for Elementary Systems
Directory of Open Access Journals (Sweden)
Daniel J. Graham
2009-12-01
Full Text Available Systems do not elect thermodynamic pathways on their own. They operate in tandem with their surroundings. Pathway selection and traversal require coordinated work and heat exchanges along with parallel tuning of the system variables. Previous research by the author (Reference [1] focused on the information expressed in thermodynamic pathways. Examined here is how spectral entropy is a by-product of information that depends intricately on the pathway structure. The spectral entropy has proven to be a valuable tool in diverse fields. This paper illustrates the contact between spectral entropy and the properties which distinguish ideal from non-ideal gases. The role of spectral entropy in the first and second laws of thermodynamics and heat → work conversions is also discussed.
Tsallis-like entropies in quantum scattering
International Nuclear Information System (INIS)
Ion, D.B.; Ion, M.L.
1998-01-01
In this work, the following entropies in quantum scattering are defined: the informational angular entropy, S θ ; Tsallis-like angular entropies, S q (θ); the angular momentum entropy, S L ; the Tsallis-like angular momentum entropies, S q (L); the angle-angular momentum entropy, S θL . These entropies are defined as natural measures of the uncertainties corresponding to the distribution probabilities. If we are interested in obtaining a measure of uncertainty of the simultaneous realization of the probability distributions, than, we have to calculate the entropy corresponding to these distributions. The expression of angle-angular momentum entropy is given. The relation between the Tsallis entropies and the angle-angular momentum entropy is derived
Introduction to maximum entropy
International Nuclear Information System (INIS)
Sivia, D.S.
1988-01-01
The maximum entropy (MaxEnt) principle has been successfully used in image reconstruction in a wide variety of fields. We review the need for such methods in data analysis and show, by use of a very simple example, why MaxEnt is to be preferred over other regularizing functions. This leads to a more general interpretation of the MaxEnt method, and its use is illustrated with several different examples. Practical difficulties with non-linear problems still remain, this being highlighted by the notorious phase problem in crystallography. We conclude with an example from neutron scattering, using data from a filter difference spectrometer to contrast MaxEnt with a conventional deconvolution. 12 refs., 8 figs., 1 tab
Introduction to maximum entropy
International Nuclear Information System (INIS)
Sivia, D.S.
1989-01-01
The maximum entropy (MaxEnt) principle has been successfully used in image reconstruction in a wide variety of fields. The author reviews the need for such methods in data analysis and shows, by use of a very simple example, why MaxEnt is to be preferred over other regularizing functions. This leads to a more general interpretation of the MaxEnt method, and its use is illustrated with several different examples. Practical difficulties with non-linear problems still remain, this being highlighted by the notorious phase problem in crystallography. He concludes with an example from neutron scattering, using data from a filter difference spectrometer to contrast MaxEnt with a conventional deconvolution. 12 refs., 8 figs., 1 tab
International Nuclear Information System (INIS)
Kandrup, H.E.
1988-01-01
The notion of a p-particle entropy Sp introduced by Kandrup (1987) is applied here to a Newtonian cosmology modeled as an expanding system of identical point masses studying the time dependence of S1 and S2 in the framework of the linearized theory considered by Fall and Saslaw (1976). It is found that if, at some initial time t0, the galaxy-galaxy correlation function vanished, then S1(t0) = S2(t0). At least for short times t - t0 thereafter, S1 and Delta S = S1 - S2 increase on a characteristic time scale. For all times t after t0, S1(t) = S2(t) or greater. 13 references
Entropy in Collisionless Self-gravitating Systems
Barnes, Eric; Williams, L.
2010-01-01
Collisionless systems, like simulated dark matter halos or gas-less elliptical galaxies, often times have properties suggesting that a common physical principle controls their evolution. For example, N-body simulations of dark matter halos present nearly scale-free density/velocity-cubed profiles. In an attempt to understand the origins of such relationships, we adopt a thermodynamics approach. While it is well-known that self-gravitating systems do not have physically realizable thermal equilibrium configurations, we are interested in the behavior of entropy as mechanical equilibrium is acheived. We will discuss entropy production in these systems from a kinetic theory point of view. This material is based upon work supported by the National Aeronautics and Space Administration under grant NNX07AG86G issued through the Science Mission Directorate.
Two faces of entropy and information in biological systems.
Mitrokhin, Yuriy
2014-10-21
The article attempts to overcome the well-known paradox of contradictions between the emerging biological organization and entropy production in biological systems. It is assumed that quality, speculative correlation between entropy and antientropy processes taking place both in the past and today in the metabolic and genetic cellular systems may be perfectly authorized for adequate description of the evolution of biological organization. So far as thermodynamic entropy itself cannot compensate for the high degree of organization which exists in the cell, we discuss the mode of conjunction of positive entropy events (mutations) in the genetic systems of the past generations and the formation of organized structures of current cells. We argue that only the information which is generated in the conditions of the information entropy production (mutations and other genome reorganization) in genetic systems of the past generations provides the physical conjunction of entropy and antientropy processes separated from each other in time generations. It is readily apparent from the requirements of the Second law of thermodynamics. Copyright © 2014 Elsevier Ltd. All rights reserved.
Lebon, G.; Jou, D.
2015-06-01
This paper gives a historical account of the early years (1953-1983) of extended irreversible thermodynamics (EIT). The salient features of this formalism are to upgrade the thermodynamic fluxes of mass, momentum, energy, and others, to the status of independent variables, and to explore the consistency between generalized transport equations and a generalized version of the second law of thermodynamics. This requires going beyond classical irreversible thermodynamics by redefining entropy and entropy flux. EIT provides deeper foundations, closer relations with microscopic formalisms, a wider spectrum of applications, and a more exciting conceptual appeal to non-equilibrium thermodynamics. We first recall the historical contributions by Maxwell, Cattaneo, and Grad on generalized transport equations. A thermodynamic theory wide enough to cope with such transport equations was independently proposed between 1953 and 1983 by several authors, each emphasizing different kinds of problems. In 1983, the first international meeting on this theory took place in Bellaterra (Barcelona). It provided the opportunity for the various authors to meet together for the first time and to discuss the common points and the specific differences of their previous formulations. From then on, a large amount of applications and theoretical confirmations have emerged. From the historical point of view, the emergence of EIT has been an opportunity to revisit the foundations and to open new avenues in thermodynamics, one of the most classical and well consolidated physical theories.
Irreversible Electroporation in a Swine Lung Model
International Nuclear Information System (INIS)
Dupuy, Damian E.; Aswad, Bassam; Ng, Thomas
2011-01-01
Purpose: This study was designed to evaluate the safety and tissue effects of IRE in a swine lung model. Methods: This study was approved by the institutional animal care committee. Nine anesthetized domestic swine underwent 15 percutaneous irreversible electroporation (IRE) lesion creations (6 with bipolar and 3 with 3–4 monopolar electrodes) under fluoroscopic guidance and with pancuronium neuromuscular blockade and EKG gating. IRE electrodes were placed into the central and middle third of the right mid and lower lobes in all animals. Postprocedure PA and lateral chest radiographs were obtained to evaluate for pneumothorax. Three animals were sacrificed at 2 weeks and six at 4 weeks. Animals underwent high-resolution CT scanning and PA and lateral radiographs 1 h before sacrifice. The treated lungs were removed en bloc, perfused with formalin, and sectioned. Gross pathologic and microscopic changes after standard hematoxylin and eosin staining were analyzed within the areas of IRE lesion creation. Results: No significant adverse events were identified. CT showed focal areas of spiculated high density ranging in greatest diameter from 1.1–2.2 cm. On gross inspection of the sectioned lung, focal areas of tan discoloration and increased density were palpated in the areas of IRE. Histological analysis revealed focal areas of diffuse alveolar damage with fibrosis and inflammatory infiltration that respected the boundaries of the interlobular septae. No pathological difference could be discerned between the 2- and 4-week time points. The bronchioles and blood vessels within the areas of IRE were intact and did not show signs of tissue injury. Conclusion: IRE creates focal areas of diffuse alveolar damage without creating damage to the bronchioles or blood vessels. Short-term safety in a swine model appears to be satisfactory.
Bubble Entropy: An Entropy Almost Free of Parameters.
Manis, George; Aktaruzzaman, Md; Sassi, Roberto
2017-11-01
Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation
The concept of entropy. Relation between action and entropy
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J.-P.Badiali
2005-01-01
Full Text Available The Boltzmann expression for entropy represents the traditional link between thermodynamics and statistical mechanics. New theoretical developments like the Unruh effect or the black hole theory suggest a new definition of entropy. In this paper we consider the thermodynamics of black holes as seriously founded and we try to see what we can learn from it in the case of ordinary systems for which a pre-relativistic description is sufficient. We introduce a space-time model and a new definition of entropy considering the thermal equilibrium from a dynamic point of view. Then we show that for black hole and ordinary systems we have the same relation relating a change of entropy to a change of action.
Zero modes and entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Yazdi, Yasaman K. [Perimeter Institute for Theoretical Physics,31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada)
2017-04-26
Ultraviolet divergences are widely discussed in studies of entanglement entropy. Also present, but much less understood, are infrared divergences due to zero modes in the field theory. In this note, we discuss the importance of carefully handling zero modes in entanglement entropy. We give an explicit example for a chain of harmonic oscillators in 1D, where a mass regulator is necessary to avoid an infrared divergence due to a zero mode. We also comment on a surprising contribution of the zero mode to the UV-scaling of the entanglement entropy.
Shannon's information is not entropy
International Nuclear Information System (INIS)
Schiffer, M.
1990-01-01
In this letter we clear up the long-standing misidentification of Shannon's Information with Entropy. We show that Information, in contrast to Entropy, is not invariant under unitary transformations and that these quantities are only equivalent for representations consisting of Hamiltonian eigenstates. We illustrate this fact through a toy system consisting of a harmonic oscillator in a coherent state. It is further proved that the representations which maximize the information are those which are energy-eigenstates. This fact sets the entropy as an upper bound for Shannon's Information. (author)
Entropy Learning in Neural Network
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Geok See Ng
2017-12-01
Full Text Available In this paper, entropy term is used in the learning phase of a neural network. As learning progresses, more hidden nodes get into saturation. The early creation of such hidden nodes may impair generalisation. Hence entropy approach is proposed to dampen the early creation of such nodes. The entropy learning also helps to increase the importance of relevant nodes while dampening the less important nodes. At the end of learning, the less important nodes can then be eliminated to reduce the memory requirements of the neural network.
Irreversible Sorption of Contaminants During Ferrihydrite Transformation
International Nuclear Information System (INIS)
Anderson, H.L.; Arthur, S.E.; Brady, P.V.; Cygan, R.T.; Nagy, K.L.; Westrich, H.R.
1999-01-01
A better understanding of the fraction of contaminants irreversibly sorbed by minerals is necessary to effectively quantify bioavailability. Ferrihydrite, a poorly crystalline iron oxide, is a natural sink for sorbed contaminants. Contaminants may be sorbed/occluded as ferrihydrite precipitates in natural waters or as it ages and transforms to more crystalline iron oxides such as goethite or hematite. Laboratory studies indicate that Cd, Co, Cr, Cu, Ni, Np, Pb, Sr, U, and Zn are irreversibly sorbed to some extent during the aging and transformation of synthetic ferrihydrite. Barium, Ra and Sr are known to sorb on ferrihydrite in the pH range of 6 to 10 and sorb more strongly at pH values above its zero point of charge (pH> 8). We will review recent literature on metal retardation, including our laboratory and modeling investigation of Ba (as an analogue for Ra) and Sr adsorption/resorption, during ferrihydrite transformation to more crystalline iron oxides. Four ferrihydrite suspensions were aged at pH 12 and 50 C with or without Ba in 0.01 M KN03 for 68 h or in 0.17 M KN03 for 3424 h. Two ferrihydrite suspensions were aged with and without Sr at pH 8 in 0.1 M KN03 at 70C. Barium or Sr sorption, or resorption, was measured by periodically centrifuging suspension subsamples, filtering, and analyzing the filtrate for Ba or Sr. Solid subsamples were extracted with 0.2 M ammonium oxalate (pH 3 in the dark) and with 6 M HCl to determine the Fe and Ba or Sr attributed to ferrihydrite (or adsorbed on the goethite/hematite stiace) and the total Fe and Ba or Sr content, respectively. Barium or Sr occluded in goethite/hematite was determined by the difference between the total Ba or Sr and the oxalate extractable Ba or Sr. The percent transformation of ferrihydrite to goethite/hematite was estimated from the ratio of oxalate and HC1 extractable Fe. All Ba was retained in the precipitates for at least 20 h. Resorption of Ba reached a maximum of 7 to 8% of the Ba2+ added for
DEFF Research Database (Denmark)
Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg
2013-01-01
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in in...
Dynamical entropy for infinite quantum systems
International Nuclear Information System (INIS)
Hudetz, T.
1990-01-01
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
The concept of entropy in landscape evolution
Leopold, Luna Bergere; Langbein, Walter Basil
1962-01-01
The concept of entropy is expressed in terms of probability of various states. Entropy treats of the distribution of energy. The principle is introduced that the most probable condition exists when energy in a river system is as uniformly distributed as may be permitted by physical constraints. From these general considerations equations for the longitudinal profiles of rivers are derived that are mathematically comparable to those observed in the field. The most probable river profiles approach the condition in which the downstream rate of production of entropy per unit mass is constant. Hydraulic equations are insufficient to determine the velocity, depths, and slopes of rivers that are themselves authors of their own hydraulic geometries. A solution becomes possible by introducing the concept that the distribution of energy tends toward the most probable. This solution leads to a theoretical definition of the hydraulic geometry of river channels that agrees closely with field observations. The most probable state for certain physical systems can also be illustrated by random-walk models. Average longitudinal profiles and drainage networks were so derived and these have the properties implied by the theory. The drainage networks derived from random walks have some of the principal properties demonstrated by the Horton analysis; specifically, the logarithms of stream length and stream numbers are proportional to stream order.
LOCAL ENTROPY FUNCTION OF DYNAMICAL SYSTEM
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İsmail TOK
2013-05-01
Full Text Available In this work, we first,define the entropy function of the topological dynamical system and investigate basic properties of this function without going into details. Let (X,A,T be a probability measure space and consider P = { pl5p2,...,pn} a finite measurable partition of all sub-sets of topological dynamical system (X,T.Then,the quantity H (P = ^ zpt is called the i=1 entropy function of finite measurable partition P.Where f-1 log t if 0 0.If diam(P < s,then the quantity L^ (T = h^ (T - h^ (T,P is called a local entropy function of topological dynamical system (X,T . In conclusion, Let (X,T and (Y,S be two topological dynamical system. If TxS is a transformation defined on the product space (XxY,TxS with (TxS(x , y = (Tx,Sy for all (x,y X x Y.Then L ^^ (TxS = L^d(T + L (S .and, we prove some fundamental properties of this function.
Phase transitions and quantum entropy
International Nuclear Information System (INIS)
Arrachea, L.; Canosa, N.; Plastino, A.; Portesi, M.; Rossignoli, R.
1990-01-01
An examination is made of the possibility to predict phase transitions of the fundamental state of finite quantum system, knowing the quantum entropy of these states, defined on the basis of the information theory. (Author). 7 refs., 3 figs
Renyi entropy and conformal defects
Energy Technology Data Exchange (ETDEWEB)
Bianchi, Lorenzo [Humboldt-Univ. Berlin (Germany). Inst. fuer Physik; Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Meineri, Marco [Scuola Normale Superiore, Pisa (Italy); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Istituto Nazionale di Fisica Nucleare, Pisa (Italy); Myers, Robert C. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Smolkin, Michael [California Univ., Berkely, CA (United States). Center for Theoretical Physics and Department of Physics
2016-04-18
We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.
Quantum entropy and special relativity.
Peres, Asher; Scudo, Petra F; Terno, Daniel R
2002-06-10
We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.
Renyi entropy and conformal defects
International Nuclear Information System (INIS)
Bianchi, Lorenzo; Myers, Robert C.; Smolkin, Michael
2016-01-01
We propose a field theoretic framework for calculating the dependence of Renyi entropies on the shape of the entangling surface in a conformal field theory. Our approach rests on regarding the corresponding twist operator as a conformal defect and in particular, we define the displacement operator which implements small local deformations of the entangling surface. We identify a simple constraint between the coefficient defining the two-point function of the displacement operator and the conformal weight of the twist operator, which consolidates a number of distinct conjectures on the shape dependence of the Renyi entropy. As an example, using this approach, we examine a conjecture regarding the universal coefficient associated with a conical singularity in the entangling surface for CFTs in any number of spacetime dimensions. We also provide a general formula for the second order variation of the Renyi entropy arising from small deformations of a spherical entangling surface, extending Mezei's results for the entanglement entropy.
Algorithmic randomness and physical entropy
International Nuclear Information System (INIS)
Zurek, W.H.
1989-01-01
Algorithmic randomness provides a rigorous, entropylike measure of disorder of an individual, microscopic, definite state of a physical system. It is defined by the size (in binary digits) of the shortest message specifying the microstate uniquely up to the assumed resolution. Equivalently, algorithmic randomness can be expressed as the number of bits in the smallest program for a universal computer that can reproduce the state in question (for instance, by plotting it with the assumed accuracy). In contrast to the traditional definitions of entropy, algorithmic randomness can be used to measure disorder without any recourse to probabilities. Algorithmic randomness is typically very difficult to calculate exactly but relatively easy to estimate. In large systems, probabilistic ensemble definitions of entropy (e.g., coarse-grained entropy of Gibbs and Boltzmann's entropy H=lnW, as well as Shannon's information-theoretic entropy) provide accurate estimates of the algorithmic entropy of an individual system or its average value for an ensemble. One is thus able to rederive much of thermodynamics and statistical mechanics in a setting very different from the usual. Physical entropy, I suggest, is a sum of (i) the missing information measured by Shannon's formula and (ii) of the algorithmic information content---algorithmic randomness---present in the available data about the system. This definition of entropy is essential in describing the operation of thermodynamic engines from the viewpoint of information gathering and using systems. These Maxwell demon-type entities are capable of acquiring and processing information and therefore can ''decide'' on the basis of the results of their measurements and computations the best strategy for extracting energy from their surroundings. From their internal point of view the outcome of each measurement is definite
Irreversible adsorption of particles on heterogeneous surfaces.
Adamczyk, Zbigniew; Jaszczółt, Katarzyna; Michna, Aneta; Siwek, Barbara; Szyk-Warszyńska, Lilianna; Zembala, Maria
2005-12-30
Methods of theoretical and experimental evaluation of irreversible adsorption of particles, e.g., colloids and globular proteins at heterogeneous surfaces were reviewed. The theoretical models were based on the generalized random sequential adsorption (RSA) approach. Within the scope of these models, localized adsorption of particles occurring as a result of short-ranged attractive interactions with discrete adsorption sites was analyzed. Monte-Carlo type simulations performed according to this model enabled one to determine the initial flux, adsorption kinetics, jamming coverage and the structure of the particle monolayer as a function of the site coverage and the particle/site size ratio, denoted by lambda. It was revealed that the initial flux increased significantly with the site coverage theta(s) and the lambda parameter. This behavior was quantitatively interpreted in terms of the scaled particle theory. It also was demonstrated that particle adsorption kinetics and the jamming coverage increased significantly, at fixed site coverage, when the lambda parameter increased. Practically, for alpha = lambda2theta(s) > 1 the jamming coverage at the heterogeneous surfaces attained the value pertinent to continuous surfaces. The results obtained prove unequivocally that spherically shaped sites were more efficient in binding particles in comparison with disk-shaped sites. It also was predicted that for particle size ratio lambda charge. Particle deposition occurred under diffusion-controlled transport conditions and their coverage was evaluated by direct particle counting using the optical and electron microscopy. Adsorption kinetics was quantitatively interpreted in terms of numerical solutions of the governing diffusion equation with the non-linear boundary condition derived from Monte-Carlo simulations. It was proven that for site coverage as low as a few percent the initial flux at heterogeneous surfaces attained the maximum value pertinent to homogeneous
Applications of Entropy in Finance: A Review
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Guanqun Tong
2013-11-01
Full Text Available Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.
Spontaneous entropy decrease and its statistical formula
Xing, Xiu-San
2007-01-01
Why can the world resist the law of entropy increase and produce self-organizing structure? Does the entropy of an isolated system always only increase and never decrease? Can be thermodymamic degradation and self-organizing evolution united? How to unite? In this paper starting out from nonequilibrium entropy evolution equation we proved that a new entropy decrease could spontaneously emerge in nonequilibrium system with internal attractive interaction. This new entropy decrease coexists wit...
Arithmetic of quantum entropy function
International Nuclear Information System (INIS)
Sen, Ashoke
2009-01-01
Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.
Mixing, entropy and competition
International Nuclear Information System (INIS)
Klimenko, A Y
2012-01-01
Non-traditional thermodynamics, applied to random behaviour associated with turbulence, mixing and competition, is reviewed and analysed. Competitive mixing represents a general framework for the study of generic properties of competitive systems and can be used to model a wide class of non-equilibrium phenomena ranging from turbulent premixed flames and invasion waves to complex competitive systems. We demonstrate consistency of the general principles of competition with thermodynamic description, review and analyse the related entropy concepts and introduce the corresponding competitive H-theorem. A competitive system can be characterized by a thermodynamic quantity—competitive potential—which determines the likely direction of evolution of the system. Contested resources tend to move between systems from lower to higher values of the competitive potential. There is, however, an important difference between conventional thermodynamics and competitive thermodynamics. While conventional thermodynamics is constrained by its zeroth law and is fundamentally transitive, the transitivity of competitive thermodynamics depends on the transitivity of the competition rules. Intransitivities are common in the real world and are responsible for complex behaviour in competitive systems. This work follows ideas and methods that have originated from the analysis of turbulent combustion, but reviews a much broader scope of issues linked to mixing and competition, including thermodynamic characterization of complex competitive systems with self-organization. The approach presented here is interdisciplinary and is addressed to the general educated readers, whereas the mathematical details can be found in the appendices. (comment)
Entropy Generation Minimization in Dimethyl Ether Synthesis: A Case Study
Kingston, Diego; Razzitte, Adrián César
2018-04-01
Entropy generation minimization is a method that helps improve the efficiency of real processes and devices. In this article, we study the entropy production (due to chemical reactions, heat exchange and friction) in a conventional reactor that synthesizes dimethyl ether and minimize it by modifying different operating variables of the reactor, such as composition, temperature and pressure, while aiming at a fixed production of dimethyl ether. Our results indicate that it is possible to reduce the entropy production rate by nearly 70 % and that, by changing only the inlet composition, it is possible to cut it by nearly 40 %, though this comes at the expense of greater dissipation due to heat transfer. We also study the alternative of coupling the reactor with another, where dehydrogenation of methylcyclohexane takes place. In that case, entropy generation can be reduced by 54 %, when pressure, temperature and inlet molar flows are varied. These examples show that entropy generation analysis can be a valuable tool in engineering design and applications aiming at process intensification and efficient operation of plant equipment.
Thermodynamic Analysis of an Irreversible Maisotsenko Reciprocating Brayton Cycle
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Fuli Zhu
2018-03-01
Full Text Available An irreversible Maisotsenko reciprocating Brayton cycle (MRBC model is established using the finite time thermodynamic (FTT theory and taking the heat transfer loss (HTL, piston friction loss (PFL, and internal irreversible losses (IILs into consideration in this paper. A calculation flowchart of the power output (P and efficiency (η of the cycle is provided, and the effects of the mass flow rate (MFR of the injection of water to the cycle and some other design parameters on the performance of cycle are analyzed by detailed numerical examples. Furthermore, the superiority of irreversible MRBC is verified as the cycle and is compared with the traditional irreversible reciprocating Brayton cycle (RBC. The results can provide certain theoretical guiding significance for the optimal design of practical Maisotsenko reciprocating gas turbine plants.
Performance Optimization of Irreversible Air Heat Pumps Considering Size Effect
Bi, Yuehong; Chen, Lingen; Ding, Zemin; Sun, Fengrui
2018-06-01
Considering the size of an irreversible air heat pump (AHP), heating load density (HLD) is taken as thermodynamic optimization objective by using finite-time thermodynamics. Based on an irreversible AHP with infinite reservoir thermal-capacitance rate model, the expression of HLD of AHP is put forward. The HLD optimization processes are studied analytically and numerically, which consist of two aspects: (1) to choose pressure ratio; (2) to distribute heat-exchanger inventory. Heat reservoir temperatures, heat transfer performance of heat exchangers as well as irreversibility during compression and expansion processes are important factors influencing on the performance of an irreversible AHP, which are characterized with temperature ratio, heat exchanger inventory as well as isentropic efficiencies, respectively. Those impacts of parameters on the maximum HLD are thoroughly studied. The research results show that HLD optimization can make the size of the AHP system smaller and improve the compactness of system.
General thermodynamic performance of irreversible absorption heat pump
International Nuclear Information System (INIS)
Zhao Xiling; Fu Lin; Zhang Shigang
2011-01-01
The absorption heat pump (AHP) was studied with thermodynamics. A four reservoirs model of absorption heat pump was established considering the heat resistance, heat leak and the internal irreversibility. The reasonable working regions, the performance effects of irreversibility, heat leak and the correlation of four components were studied. When studying the effects of internal irreversibility, two internal irreversibility parameters (I he for generator-absorber assembly and I re for evaporator-condenser assembly) were introduced to distinguish the different effects. When studying the heat transfer relations of four components, a universal relationship between the main parameters were deduced. The results which have more realized meaning show that, the reduction of the friction, heat loss, and internal dissipations of the evaporator-condenser assembly are more important than its reduction of generator-absorber assembly, and lessening the heat leak of generator are more important than its reduction of other components to improve the AHP performance.
Irreversibility and dissipation in finite-state automata
International Nuclear Information System (INIS)
Ganesh, Natesh; Anderson, Neal G.
2013-01-01
Irreversibility and dissipation in finite-state automata (FSA) are considered from a physical-information-theoretic perspective. A quantitative measure for the computational irreversibility of finite automata is introduced, and a fundamental lower bound on the average energy dissipated per state transition is obtained and expressed in terms of FSA irreversibility. The irreversibility measure and energy bound are germane to any realization of a deterministic automaton that faithfully registers abstract FSA states in distinguishable states of a physical system coupled to a thermal environment, and that evolves via a sequence of interactions with an external system holding a physical instantiation of a random input string. The central result, which is shown to follow from quantum dynamics and entropic inequalities alone, can be regarded as a generalization of Landauer's Principle applicable to FSAs and tailorable to specified automata. Application to a simple FSA is illustrated.
Eu, Byung Chan
2016-01-01
This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respe...
Anisotropic shift of the irreversibility line by neutron irradiation
International Nuclear Information System (INIS)
Sauerzopf, F.M.; Wiesinger, H.P.; Weber, H.W.; Crabtree, G.W.; Frischherz, M.C.; Kirk, M.A.
1991-09-01
The irreversibility line of high-T c superconductors is shifted considerably by irradiating the material with fast neutrons. The anisotropic and non-monotonous shift is qualitatively explained by a simple model based on an interaction between three pinning mechanisms, the intrinsic pinning by the ab-planes, the weak pinning by the pre-irradiation defect structure, and strong pinning by neutron induced defect cascades. A correlation between the cascade density and the position of the irreversibility line is observed
Irreversibility and higher-spin conformal field theory
Anselmi, D
2000-01-01
I discuss the idea that quantum irreversibility is a general principle of nature and a related "conformal hypothesis", stating that all fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points. In particular, the Newton constant should be viewed as a low-energy effect of the RG scale. This approach leads naturally to consider higher-spin conformal field theories, which are here classified, as candidate high-energy theories. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. The central charges c and a are well defined and positive. I calculate their values and study the operator-product structure. Fermionic theories have no gauge invariance and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a...
Quantum key distribution with finite resources: Smooth Min entropy vs. Smooth Renyi entropy
Energy Technology Data Exchange (ETDEWEB)
Mertz, Markus; Abruzzo, Silvestre; Bratzik, Sylvia; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Duesseldorf (Germany)
2010-07-01
We consider different entropy measures that play an important role in the analysis of the security of QKD with finite resources. The smooth min entropy leads to an optimal bound for the length of a secure key. Another bound on the secure key length was derived by using Renyi entropies. Unfortunately, it is very hard or even impossible to calculate these entropies for realistic QKD scenarios. To estimate the security rate it becomes important to find computable bounds on these entropies. Here, we compare a lower bound for the smooth min entropy with a bound using Renyi entropies. We compare these entropies for the six-state protocol with symmetric attacks.
Jarzynski equality in the context of maximum path entropy
González, Diego; Davis, Sergio
2017-06-01
In the global framework of finding an axiomatic derivation of nonequilibrium Statistical Mechanics from fundamental principles, such as the maximum path entropy - also known as Maximum Caliber principle -, this work proposes an alternative derivation of the well-known Jarzynski equality, a nonequilibrium identity of great importance today due to its applications to irreversible processes: biological systems (protein folding), mechanical systems, among others. This equality relates the free energy differences between two equilibrium thermodynamic states with the work performed when going between those states, through an average over a path ensemble. In this work the analysis of Jarzynski's equality will be performed using the formalism of inference over path space. This derivation highlights the wide generality of Jarzynski's original result, which could even be used in non-thermodynamical settings such as social systems, financial and ecological systems.
Directory of Open Access Journals (Sweden)
Milivoje M. Kostic
2016-01-01
Full Text Available There is a growing trend in recently-submitted manuscripts and publications to present calculated results of entropy generation, also known as entropy production, as field quantities in a system or device control volume, based on prior calculation of velocity and temperature fields, frequently using CFD numerical methods. [...
Jesudason, Christopher G.
2003-09-01
Recently, there have appeared interesting correctives or challenges [Entropy 1999, 1, 111-147] to the Second law formulations, especially in the interpretation of the Clausius equivalent transformations, closely related in area to extensions of the Clausius principle to irreversible processes [Chem. Phys. Lett. 1988, 143(1), 65-70]. Since the traditional formulations are central to science, a brief analysis of some of these newer theories along traditional lines is attempted, based on well-attested axioms which have formed the basis of equilibrium thermodynamics. It is deduced that the Clausius analysis leading to the law of increasing entropy does not follow from the given axioms but it can be proved that for irreversible transitions, the total entropy change of the system and thermal reservoirs (the "Universe") is not negative, even for the case when the reservoirs are not at the same temperature as the system during heat transfer. On the basis of two new simple theorems and three corollaries derived for the correlation between irreversible and reversible pathways and the traditional axiomatics, it is shown that a sequence of reversible states can never be used to describe a corresponding sequence of irreversible states for at least closed systems, thereby restricting the principle of local equilibrium. It is further shown that some of the newer irreversible entropy forms given exhibit some paradoxical properties relative to the standard axiomatics. It is deduced that any reconciliation between the traditional approach and novel theories lie in creating a well defined set of axioms to which all theoretical developments should attempt to be based on unless proven not be useful, in which case there should be consensus in removing such axioms from theory. Clausius' theory of equivalent transformations do not contradict the traditional understanding of heat- work efficiency. It is concluded that the intuitively derived assumptions over the last two centuries seem to
Maximum Entropy in Drug Discovery
Directory of Open Access Journals (Sweden)
Chih-Yuan Tseng
2014-07-01
Full Text Available Drug discovery applies multidisciplinary approaches either experimentally, computationally or both ways to identify lead compounds to treat various diseases. While conventional approaches have yielded many US Food and Drug Administration (FDA-approved drugs, researchers continue investigating and designing better approaches to increase the success rate in the discovery process. In this article, we provide an overview of the current strategies and point out where and how the method of maximum entropy has been introduced in this area. The maximum entropy principle has its root in thermodynamics, yet since Jaynes’ pioneering work in the 1950s, the maximum entropy principle has not only been used as a physics law, but also as a reasoning tool that allows us to process information in hand with the least bias. Its applicability in various disciplines has been abundantly demonstrated. We give several examples of applications of maximum entropy in different stages of drug discovery. Finally, we discuss a promising new direction in drug discovery that is likely to hinge on the ways of utilizing maximum entropy.
Attribution of irreversible loss to anthropogenic climate change
Huggel, Christian; Bresch, David; Hansen, Gerrit; James, Rachel; Mechler, Reinhard; Stone, Dáithí; Wallimann-Helmer, Ivo
2016-04-01
The Paris Agreement (2015) under the UNFCCC has anchored loss and damage in a separate article which specifies that understanding and support should be enhanced in areas addressing loss and damage such as early warning, preparedness, insurance and resilience. Irreversible loss is a special category under loss and damage but there is still missing clarity over what irreversible loss actually includes. Many negative impacts of climate change may be handled or mitigated by existing risk management, reduction and absorption approaches. Irreversible loss, however, is thought to be insufficiently addressed by risk management. Therefore, countries potentially or actually affected by irreversible loss are calling for other measures such as compensation, which however is highly contested in international climate policy. In Paris (2015) a decision was adopted that loss and damage as defined in the respective article of the agreement does not involve compensation and liability. Nevertheless, it is likely that some sort of mechanism will eventually need to come into play for irreversible loss due to anthropogenic climate change, which might involve compensation, other forms of non-monetary reparation, or transformation. Furthermore, climate litigation has increasingly been attempted to address negative effects of climate change. In this context, attribution is important to understand the drivers of change, what counts as irreversible loss due to climate change, and, possibly, who or what is responsible. Here we approach this issue by applying a detection and attribution perspective on irreversible loss. We first analyze detected climate change impacts as assessed in the IPCC Fifth Assessment Report. We distinguish between irreversible loss in physical, biological and human systems, and accordingly identify the following candidates of irreversible loss in these systems: loss of glaciers and ice sheets, loss of subsurface ice (permafrost) and related loss of lake systems; loss
Thermodynamic extremal principles for irreversible processes in materials science
Czech Academy of Sciences Publication Activity Database
Fischer, F. D.; Svoboda, Jiří; Petryk, H.
2014-01-01
Roč. 67, APR (2014), s. 1-20 ISSN 1359-6454 Institutional support: RVO:68081723 Keywords : Non- equilibrium * Thermodynamics * Entropy * Onsager's principle * Thermodynamic extremal principles Subject RIV: BJ - Thermodynamics Impact factor: 4.465, year: 2014
Lemons, Don S
2013-01-01
Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Nearly 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.
Shannon entropy and particle decays
Carrasco Millán, Pedro; García-Ferrero, M. Ángeles; Llanes-Estrada, Felipe J.; Porras Riojano, Ana; Sánchez García, Esteban M.
2018-05-01
We deploy Shannon's information entropy to the distribution of branching fractions in a particle decay. This serves to quantify how important a given new reported decay channel is, from the point of view of the information that it adds to the already known ones. Because the entropy is additive, one can subdivide the set of channels and discuss, for example, how much information the discovery of a new decay branching would add; or subdivide the decay distribution down to the level of individual quantum states (which can be quickly counted by the phase space). We illustrate the concept with some examples of experimentally known particle decay distributions.
Text mining by Tsallis entropy
Jamaati, Maryam; Mehri, Ali
2018-01-01
Long-range correlations between the elements of natural languages enable them to convey very complex information. Complex structure of human language, as a manifestation of natural languages, motivates us to apply nonextensive statistical mechanics in text mining. Tsallis entropy appropriately ranks the terms' relevance to document subject, taking advantage of their spatial correlation length. We apply this statistical concept as a new powerful word ranking metric in order to extract keywords of a single document. We carry out an experimental evaluation, which shows capability of the presented method in keyword extraction. We find that, Tsallis entropy has reliable word ranking performance, at the same level of the best previous ranking methods.
Methods for calculating nonconcave entropies
International Nuclear Information System (INIS)
Touchette, Hugo
2010-01-01
Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: (i) microcanonical contraction, (ii) metastable branches of the free energy, (iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, (iv) the restricted canonical ensemble, and (v) the inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method
Kang, Dun-Yen; Liou, Kai-Hsin; Chang, Wei-Lun
2015-01-01
The expansion or compression of gas confined in a piston-and-cylinder device is a classic working example used for illustrating the First and Second Laws of Thermodynamics. The balance of energy and entropy enables the estimation of a number of thermodynamic properties. The entropy generation (also called entropy production) resulting from this…
Irreversible climate change due to carbon dioxide emissions
Solomon, Susan; Plattner, Gian-Kasper; Knutti, Reto; Friedlingstein, Pierre
2009-01-01
The severity of damaging human-induced climate change depends not only on the magnitude of the change but also on the potential for irreversibility. This paper shows that the climate change that takes place due to increases in carbon dioxide concentration is largely irreversible for 1,000 years after emissions stop. Following cessation of emissions, removal of atmospheric carbon dioxide decreases radiative forcing, but is largely compensated by slower loss of heat to the ocean, so that atmospheric temperatures do not drop significantly for at least 1,000 years. Among illustrative irreversible impacts that should be expected if atmospheric carbon dioxide concentrations increase from current levels near 385 parts per million by volume (ppmv) to a peak of 450–600 ppmv over the coming century are irreversible dry-season rainfall reductions in several regions comparable to those of the “dust bowl” era and inexorable sea level rise. Thermal expansion of the warming ocean provides a conservative lower limit to irreversible global average sea level rise of at least 0.4–1.0 m if 21st century CO2 concentrations exceed 600 ppmv and 0.6–1.9 m for peak CO2 concentrations exceeding ≈1,000 ppmv. Additional contributions from glaciers and ice sheet contributions to future sea level rise are uncertain but may equal or exceed several meters over the next millennium or longer. PMID:19179281
Examples of Entropy-driven Ordering
Indian Academy of Sciences (India)
driven Ordering. Orientational ordering of long objects. Entropy of sliding increases. Freezing in hard-sphere systems. Vibrational entropy increases. Phase separation in hard-sphere binary mixtures with disparate sizes. More room for smaller ...
Using entropy measures to characterize human locomotion.
Leverick, Graham; Szturm, Tony; Wu, Christine Q
2014-12-01
Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five considered entropy measures increase meaningfully with the increased probability of falling in a simple passive bipedal walker model. The same four entropy measures also experienced statistically significant increases in response to increasing age and gait impairment caused by cognitive interference in an experimental study. Of the considered entropy measures, the proposed quantized dynamical entropy (QDE) and quantization-based approximation of sample entropy (QASE) offered the best combination of sensitivity to changes in gait dynamics and computational efficiency. Based on these results, entropy appears to be a viable candidate for assessing the stability of human locomotion.
On thermodynamic limits of entropy densities
Moriya, H; Van Enter, A
We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.
Multivariate refined composite multiscale entropy analysis
International Nuclear Information System (INIS)
Humeau-Heurtier, Anne
2016-01-01
Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE. - Highlights: • Multiscale entropy quantifies data complexity but may be inaccurate at large scale. • A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. • Nevertheless, RCMSE is adapted to univariate time series only. • We herein introduce an extension of RCMSE to multivariate data. • It shows better performances than the standard multivariate multiscale entropy.
The entropy principle thermodynamics for the unsatisfied
Thess, André
2011-01-01
Entropy is the most important and the most difficult to understand term of thermodynamics. This book helps make this key concept understandable. It includes seven illustrative examples of applications of entropy, which are presented step by step.
A brief introduction to sofic entropy theory
Bowen, Lewis
2017-01-01
Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.
Notes on entanglement entropy in string theory
International Nuclear Information System (INIS)
He, Song; Numasawa, Tokiro; Takayanagi, Tadashi; Watanabe, Kento
2015-01-01
In this paper, we study the conical entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the conical entropy in closed superstring is UV finite owing to the string scale cutoff.
Uncertainty principle and informational entropy for partially coherent light
Bastiaans, M.J.
1986-01-01
It is shown that, among all partially coherent wave fields having the same informational entropy, the product of the effective widths of the intensity functions in the space and the spatial-frequency domains takes its minimum value for a wave field with a Gaussian-shaped cross-spectral density
Short interval expansion of Rényi entropy on torus
Energy Technology Data Exchange (ETDEWEB)
Chen, Bin [Department of Physics and State Key Laboratory of Nuclear Physics and Technology,Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Collaborative Innovation Center of Quantum Matter,5 Yiheyuan Rd, Beijing 100871 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Wu, Jun-Bao [Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Center for High Energy Physics, Peking University,5 Yiheyuan Rd, Beijing 100871 (China); Zhang, Jia-ju [Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China)
2016-08-23
We investigate the short interval expansion of the Rényi entropy for two-dimensional conformal field theory (CFT) on a torus. We require the length of the interval ℓ to be small with respect to the spatial and temporal sizes of the torus. The operator product expansion of the twist operators allows us to compute the short interval expansion of the Rényi entropy at any temperature. In particular, we pay special attention to the large c CFTs dual to the AdS{sub 3} gravity and its cousins. At both low and high temperature limits, we read the Rényi entropies to order ℓ{sup 6}, and find good agreements with holographic results. Moreover, the expansion allows us to read 1/c contribution, which is hard to get by expanding the thermal density matrix. We generalize the study to the case with the chemical potential as well.
Reversible and Irreversible Binding of Nanoparticles to Polymeric Surfaces
Directory of Open Access Journals (Sweden)
Wolfgang H. Binder
2009-01-01
Full Text Available Reversible and irreversible binding of CdSe-nanoparticles and nanorods to polymeric surfaces via a strong, multiple hydrogen bond (= Hamilton-receptor/barbituric acid is described. Based on ROMP-copolymers, the supramolecular interaction on a thin polymer film is controlled by living polymerization methods, attaching the Hamilton-receptor in various architectures, and concentrations. Strong binding is observed with CdSe-nanoparticles and CdSe-nanorods, whose surfaces are equipped with matching barbituric acid-moieties. Addition of polar solvents, able to break the hydrogen bonds leads to the detachment of the nanoparticles from the polymeric film. Irreversible binding is observed if an azide/alkine-“click”-reaction is conducted after supramolecular recognition of the nanoparticles on the polymeric surface. Thus reversible or irreversible attachment of the nanosized objects can be achieved.
Spectral line intensity irreversibility in circulatory plasma magnetization processes
Qu, Z. Q.; Dun, G. T.
2012-01-01
Spectral line intensity variation is found to be irreversible in circulatory plasma magnetization process by experiments described in this paper, i.e., the curves illustrating spectral line photon fluxes irradiated from a light source immerged in a magnetic field by increasing the magnetic induction cannot be reproduced by decreasing the magnetic induction within the errors. There are two plasma magnetization patterns found. One shows that the intensities are greater at the same magnetic inductions during the magnetic induction decreasing process after the increasing, and the other gives the opposite effect. This reveals that the magneto-induced excitation and de-excitation process is irreversible like ferromagnetic magnetization. But the two irreversible processes are very different in many aspects stated in the text.
Definition of Nonequilibrium Entropy of General Systems
Mei, Xiaochun
1999-01-01
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in the paper. The result shows that the definition of nonequilibrium entropy is not unique.
Logical entropy of quantum dynamical systems
Directory of Open Access Journals (Sweden)
Ebrahimzadeh Abolfazl
2016-01-01
Full Text Available This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.
The Wehrl entropy has Gaussian optimizers
DEFF Research Database (Denmark)
De Palma, Giacomo
2018-01-01
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...
Algebraic entropy for differential-delay equations
Viallet, Claude M.
2014-01-01
We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.
Universal canonical entropy for gravitating systems
Indian Academy of Sciences (India)
Similar to this is the case of ref. [12] which also uses the saddle point approximation to express the microcanonical entropy in terms of the canonical entropy [12a]. Recalling that there is at least 'circumstantial' evidence that the microcanonical entropy has a 'universal' form [13–15], identical to that obtained in ref. [6] quoted.
Regularities of changes of metal melting entropy
International Nuclear Information System (INIS)
Kats, S.A.; Chekhovskoj, V.Ya.
1980-01-01
Most trustworthy data on temperatures, heats and entropies of fusion of metals have been used as a basis to throw light on the laws governing variations of the entropy of metals fusion. The elaborated procedure is used to predict the entropies of the metals fusion whose thermodynamic properties under high temperatures have not yet been investigated
Single Particle Entropy in Heated Nuclei
International Nuclear Information System (INIS)
Guttormsen, M.; Chankova, R.; Hjorth-Jensen, M.; Rekstad, J.; Siem, S.; Sunde, A. C.; Syed, N. U. H.; Agvaanluvsan, U.; Schiller, A.; Voinov, A.
2006-01-01
The thermal motion of single particles represents the largest contribution to level density (or entropy) in atomic nuclei. The concept of single particle entropy is presented and shown to be an approximate extensive (additive) quantity for mid-shell nuclei. A few applications of single particle entropy are demonstrated
The dynamical entropy of quantum systems
International Nuclear Information System (INIS)
Connes, A.; Narnhofer, H.; Thirring, W.
1987-01-01
The definition of the dynamical entropy for automorphisms of C * - algebras is represented. Several properties are discussed; especially it is argued that the entropy of the shift can be shown in special cases to be equal with the entropy density. (Author)
Shang, Ran
2015-05-06
The application of ceramic membranes in water treatment is becoming increasing attractive because of their long life time and excellent chemical, mechanical and thermal stability. However, fouling of ceramic membranes, especially hydraulically irreversible fouling, is still a critical aspect affecting the operational cost and energy consumption in water treatment plants. In this study, four ceramic membranes with pore sizes or molecular weight cut-off (MWCO) of 0.20 μm, 0.14 μm, 300 kDa and 50 kDa were compared during natural surface water filtration with respect to hydraulically irreversible fouling index (HIFI), foulant composition and narrowing of pore size due to the irreversible fouling. Our results showed that the hydraulically irreversible fouling index (HIFI) was proportional to the membrane pore size (r2=0.89) when the same feed water was filtrated. The UF membranes showed lower HIFI values than the MF membranes. Pore narrowing (internal fouling) was found to be a main fouling pattern of the hydraulically irreversible fouling. The internal fouling was caused by monolayer adsorption of foulants with different sizes that is dependent on the size of the membrane pore.
Shang, Ran; Vuong, Francois; Hu, Jingyi; Li, Sheng; Kemperman, Antoine J.B.; Nijmeijer, Kitty; Cornelissen, Emile R.; Heijman, Sebastiaan G.J.; Rietveld, Luuk C.
2015-01-01
The application of ceramic membranes in water treatment is becoming increasing attractive because of their long life time and excellent chemical, mechanical and thermal stability. However, fouling of ceramic membranes, especially hydraulically irreversible fouling, is still a critical aspect affecting the operational cost and energy consumption in water treatment plants. In this study, four ceramic membranes with pore sizes or molecular weight cut-off (MWCO) of 0.20 μm, 0.14 μm, 300 kDa and 50 kDa were compared during natural surface water filtration with respect to hydraulically irreversible fouling index (HIFI), foulant composition and narrowing of pore size due to the irreversible fouling. Our results showed that the hydraulically irreversible fouling index (HIFI) was proportional to the membrane pore size (r2=0.89) when the same feed water was filtrated. The UF membranes showed lower HIFI values than the MF membranes. Pore narrowing (internal fouling) was found to be a main fouling pattern of the hydraulically irreversible fouling. The internal fouling was caused by monolayer adsorption of foulants with different sizes that is dependent on the size of the membrane pore.
Irreversibility and higher-spin conformal field theory
Anselmi, Damiano
2000-08-01
I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.
Directory of Open Access Journals (Sweden)
Wassim M. Haddad
2012-02-01
Full Text Available In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we establish the existence of a unique, continuously differentiable global entropy function for our dynamical system model, and using Lyapunov stability theory we show that the proposed thermodynamic model has finite-time convergent trajectories to Lyapunov stable equilibria determined by the system initial energies. Finally, using the system entropy, we establish the absence of Poincaré recurrence for our thermodynamic model and develop clear and rigorous connections between irreversibility, the second law of thermodynamics, and the entropic arrow of time.
Entropy-driven phase transitions
Frenkel, D.
1999-01-01
Increase in visible order can be associated with an increase in microscopic disorder. This phenomenon leads to many counter-intuitive phenomena such as entropy driven crystallization and phase separation. I devote special attention to the entropic depletion interaction as a means to tune the range
Properties of von Neumann entropy
Indian Academy of Sciences (India)
disentangled) as seen by moving observers, is used to investigate the properties of von Neumann entropy, as a measure of spin–momentum entanglement. To do so, we partition the total Hilbert space into momentum and spin subspaces so that the ...
Entropy, Coding and Data Compression
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy, Coding and Data Compression. S Natarajan. General Article Volume 6 Issue 9 September 2001 pp 35-45. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0035-0045 ...
Entropy of dynamical social networks
Zhao, Kun; Karsai, Marton; Bianconi, Ginestra
2012-02-01
Dynamical social networks are evolving rapidly and are highly adaptive. Characterizing the information encoded in social networks is essential to gain insight into the structure, evolution, adaptability and dynamics. Recently entropy measures have been used to quantify the information in email correspondence, static networks and mobility patterns. Nevertheless, we still lack methods to quantify the information encoded in time-varying dynamical social networks. In this talk we present a model to quantify the entropy of dynamical social networks and use this model to analyze the data of phone-call communication. We show evidence that the entropy of the phone-call interaction network changes according to circadian rhythms. Moreover we show that social networks are extremely adaptive and are modified by the use of technologies such as mobile phone communication. Indeed the statistics of duration of phone-call is described by a Weibull distribution and is significantly different from the distribution of duration of face-to-face interactions in a conference. Finally we investigate how much the entropy of dynamical social networks changes in realistic models of phone-call or face-to face interactions characterizing in this way different type human social behavior.
Maximum entropy beam diagnostic tomography
International Nuclear Information System (INIS)
Mottershead, C.T.
1985-01-01
This paper reviews the formalism of maximum entropy beam diagnostic tomography as applied to the Fusion Materials Irradiation Test (FMIT) prototype accelerator. The same formalism has also been used with streak camera data to produce an ultrahigh speed movie of the beam profile of the Experimental Test Accelerator (ETA) at Livermore. 11 refs., 4 figs
Maximum entropy beam diagnostic tomography
International Nuclear Information System (INIS)
Mottershead, C.T.
1985-01-01
This paper reviews the formalism of maximum entropy beam diagnostic tomography as applied to the Fusion Materials Irradiation Test (FMIT) prototype accelerator. The same formalism has also been used with streak camera data to produce an ultrahigh speed movie of the beam profile of the Experimental Test Accelerator (ETA) at Livermore
Hidden states and hidden entropy
International Nuclear Information System (INIS)
Betak, E.
1993-06-01
We study the properties of master equations of the pre-equilibrium exciton model. For the case when the emission is included, we have proved the entropy to be a nondecreasing function of time. The opposite statement in the recent paper of Pan et al. has been caused mainly by neglecting a part of the exciton states. (author). 17 refs
Vibrational entropies in metallic alloys
Ozolins, Vidvuds; Asta, Mark; Wolverton, Christopher
2000-03-01
Recently, it has been recognized that vibrational entropy can have significant effects on the phase stability of metallic alloys. Using density functional linear response calculations and molecular dynamics simulations we study three representative cases: (i) phase diagram of Al-rich Al-Sc alloys, (ii) stability of precipitate phases in CuAl_2, and (iii) phonon dynamics in bcc Zr. We find large vibrational entropy effects in all cases. In the Al-Sc system, vibrations increase the solid solubility of Sc in Al by decreasing the stability of the L12 (Al_3Sc) phase. This leads to a nearly ten-fold increase in the solid solubility of Sc in Al at T=800 K. In the Cu-Al system, our calculations predict that the tetragonal Laves phase of CuAl2 has 0.35 kB/atom higher vibrational entropy than the cubic CaF_2-type phase (the latter is predicted to be the T=0 K ground state of CuAl_2). This entropy difference causes a structural transformation in CuAl2 precipitates from the fluorite to the tetragonal Laves phase around T=500 K. Finally, we analyze the highly unusual dynamics of anharmonically stabilized bcc Zr, finding large diffuse-scattering intensity streaks between the bcc Bragg peaks.
International Nuclear Information System (INIS)
Ko, T.H.
2006-01-01
In the present paper, the entropy generation and optimal Reynolds number for developing forced convection in a double sine duct with various wall heat fluxes, which frequently occurs in plate heat exchangers, are studied based on the entropy generation minimization principle by analytical thermodynamic analysis as well as numerical investigation. According to the thermodynamic analysis, a very simple expression for the optimal Reynolds number for the double sine duct as a function of mass flow rate, wall heat flux, working fluid and geometric dimensions is proposed. In the numerical simulations, the investigated Reynolds number (Re) covers the range from 86 to 2000 and the wall heat flux (q'') varies as 160, 320 and 640 W/m 2 . From the numerical simulation of the developing laminar forced convection in the double sine duct, the effect of Reynolds number on entropy generation in the duct has been examined, through which the optimal Reynolds number with minimal entropy generation is detected. The optimal Reynolds number obtained from the analytical thermodynamic analysis is compared with the one from the numerical solutions and is verified to have a similar magnitude of entropy generation as the minimal entropy generation predicted by the numerical simulations. The optimal analysis provided in the present paper gives worthy information for heat exchanger design, since the thermal system could have the least irreversibility and best exergy utilization if the optimal Re can be used according to practical design conditions
A new approach to irreversibility in deep inelastic collisions
International Nuclear Information System (INIS)
Nemes, M.C.
1982-01-01
We use concepts of statistical mechanics to discuss the irreversible character of the experimental data in deep inelastic collisions. A definition of irreversibility proposed by Ruch permits a unified overview on current theories which describe these reactions. An information theoretical analysis of the data leads to a Fokker-Planck equation for the collective variables (excitation energy, charge and mass). The concept of mixing distance can serve as a quantitative measure to characterize the 'approach to equilibrium'. We apply it to the brownian motion as an illustration and also to the phenomenological analysis of deep inelastic scattering data with interesting results. (orig.)
The thermomechanics of nonlinear irreversible behaviors an introduction
Maugin, Gérard A
1999-01-01
In this invaluable book, macroscopic irreversible thermodynamics is presented in its realm and its splendor by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviors is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of "irreversible thermodynamics" behaviors which until now have been commonly considered either not easily cove
Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making
Institute of Scientific and Technical Information of China (English)
CHENG Qi-yue; QIU Wan-hua; LIU Xiao-feng
2002-01-01
In this paper, aggregation question based on group decision making and a single decision making is studied. The theory of entropy is applied to the sets pair analysis. The system of relation entropy and the transferable entropy notion are put. The character is studied. An potential by the relation entropy and transferable entropy are defined. It is the consistency measure on the group between a single decision making. We gained a new aggregation effective definition on the group misjudge.
Directory of Open Access Journals (Sweden)
Emmanuel O.B. Ogedengbe
2012-12-01
Full Text Available Parametric studies of the effects of slip irreversibility in concentrating solar power (CSP-powered bio-digester assemblies are investigated. Complexities regarding the identification of the appropriate electro-kinetic phenomena for certain electrolyte phases are reviewed. The application of exergy analysis to the design of energy conversion devices, like solar thermal collectors, for the required heat of formation in a downdraft waste food bio-digester, is discussed. Thermal management in the silicon-based substrate of the energy system is analyzed. The rectangular-shaped micro-channels are simulated with a finite-volume, staggered coupling of the pressure-velocity fields. Entropy generation transport within the energy system is determined and coupled with the solution procedure. Consequently, the effects of channel size perturbation, Reynolds number, and pressure ratios on the thermal performance and exergy destruction are presented. A comparative analysis of the axial heat conduction for thermal management in energy conversion devices is proposed.
Entropy and Multifractality in Relativistic Ion-Ion Collisions
Directory of Open Access Journals (Sweden)
Shaista Khan
2018-01-01
Full Text Available Entropy production in multiparticle systems is investigated by analyzing the experimental data on ion-ion collisions at AGS and SPS energies and comparing the findings with those reported earlier for hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It is observed that the entropy produced in limited and full phase space, when normalized to maximum rapidity, exhibits a kind of scaling which is nicely supported by Monte Carlo model HIJING. Using Rényi’s order q information entropy, multifractal characteristics of particle production are examined in terms of generalized dimensions, Dq. Nearly the same values of multifractal specific heat, c, observed in hadronic and ion-ion collisions over a wide range of incident energies suggest that the quantity c might be used as a universal characteristic of multiparticle production in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. The analysis is extended to the study of spectrum of scaling indices. The findings reveal that Rényi’s order q information entropy could be another way to investigate the fluctuations in multiplicity distributions in terms of spectral function f(α, which has been argued to be a convenient function for comparison sake not only among different experiments but also between the data and theoretical models.
Enthalpy-entropy compensation in protein unfolding
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Enthalpy-entropy compensation was found to be a universal law in protein unfolding based on over 3 000 experimental data. Water molecular reorganization accompanying the protein unfolding was suggested as the origin of the enthalpy-entropy compensation in protein unfolding. It is indicated that the enthalpy-entropy compensation constitutes the physical foundation that satisfies the biological need of the small free energy changes in protein unfolding, without the sacrifice of the bio-diversity of proteins. The enthalpy-entropy compensation theory proposed herein also provides valuable insights into the Privalov's puzzle of enthalpy and entropy convergence in protein unfolding.
Receiver function estimated by maximum entropy deconvolution
Institute of Scientific and Technical Information of China (English)
吴庆举; 田小波; 张乃铃; 李卫平; 曾融生
2003-01-01
Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.
Controlling the Shannon Entropy of Quantum Systems
Xing, Yifan; Wu, Jun
2013-01-01
This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819
Entropy evaporated by a black hole
International Nuclear Information System (INIS)
Zurek, W.H.
1982-01-01
It is shown that the entropy of the radiation evaporated by an uncharged, nonrotating black hole into vacuum in the course of its lifetime is approximately (4/3) times the initial entropy of this black hole. Also considered is a thermodynamically reversible process in which an increase of black-hole entropy is equal to the decrease of the entropy of its surroundings. Implications of these results for the generalized second law of thermodynamics and for the interpretation of black-hole entropy are pointed out
q-entropy for symbolic dynamical systems
International Nuclear Information System (INIS)
Zhao, Yun; Pesin, Yakov
2015-01-01
For symbolic dynamical systems we use the Carathéodory construction as described in (Pesin 1997 Dimension Theory in Dynamical Systems, ConTemporary Views and Applications (Chicago: University of Chicago Press)) to introduce the notions of q-topological and q-metric entropies. We describe some basic properties of these entropies and in particular, discuss relations between q-metric entropy and local metric entropy. Both q-topological and q-metric entropies are new invariants respectively under homeomorphisms and metric isomorphisms of dynamical systems. (paper)
Holographic charged Rényi entropies
Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander; Matsuura, Shunji; Myers, Robert C.; Sierens, Todd
2013-12-01
We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.
Controlling the Shannon Entropy of Quantum Systems
Directory of Open Access Journals (Sweden)
Yifan Xing
2013-01-01
Full Text Available This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.
Entropy-Corrected Holographic Dark Energy
International Nuclear Information System (INIS)
Wei Hao
2009-01-01
The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called 'entropy-corrected holographic dark energy' (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called 'entropy-corrected agegraphic dark energy' (ECADE). (geophysics, astronomy, and astrophysics)
International Nuclear Information System (INIS)
Zhai, Y.L.; Xia, G.D.; Liu, X.F.; Wang, J.
2015-01-01
Highlights: • A novel DL-MCHS with complex structure is presented. • A model of entropy generation rate of DL-MCHSs is derived from the first and second laws of thermodynamics. • DL-MCHSs show better thermodynamic advantage and thermal performance under large volumetric flow rate. - Abstract: A new type of double-layered micro heat sink (DL-MCHS) with complex structure is designed and investigated numerically. Moreover, a model of entropy generation rate of DL-MCHSs is also derived from the first and second laws of thermodynamics. Results for the relationship of entropy generation rate between the first and second layer of DL-MCHSs, total entropy generation rate, the average temperature on the bottom wall, thermal resistance and pressure drop are investigated in detail, respectively. The results indicate that the effect of entropy generation rate of the first layer on total entropy generation rate is dominant. The thermal characteristic of DL-MCHSs with complex structure is better than that of all DL-MCHSs and single-layered micro heat sinks (SL-MCHSs) with simple structure under the same volumetric flow rate. However, DL-MCHSs only show better thermodynamic advantage and thermal performance than SL-MCHSs with complex structure when the volumetric flow rate larger than a certain value. It is not reasonable to use DL-MCHSs for cooling microelectronic equipments under small volumetric flow rate due to the larger irreversibility. Finally, the pressure drop of DL-MHCSs can be reduced by properly changing the channel height under various volumetric flow rates. Due to the less irreversibility and more uniform temperature distribution on the bottom wall, DL-MCHSs can effectively eliminate the internal thermal stresses in microelectronic equipments. Therefore, DL-MCHSs are an alternative method for the electronic cooling. Moreover, the thermodynamic analysis provides references for the actual application design
International Nuclear Information System (INIS)
Zhou, Junle; Chen, Lingen; Ding, Zemin; Sun, Fengrui
2016-01-01
Ecological performance of a single resonance ESE heat engine with heat leakage is conducted by applying finite time thermodynamics. By introducing Nielsen function and numerical calculations, expressions about power output, efficiency, entropy generation rate and ecological objective function are derived; relationships between ecological objective function and power output, between ecological objective function and efficiency as well as between power output and efficiency are demonstrated; influences of system parameters of heat leakage, boundary energy and resonance width on the optimal performances are investigated in detail; a specific range of boundary energy is given as a compromise to make ESE heat engine system work at optimal operation regions. Comparing performance characteristics with different optimization objective functions, the significance of selecting ecological objective function as the design objective is clarified specifically: when changing the design objective from maximum power output into maximum ecological objective function, the improvement of efficiency is 4.56%, while the power output drop is only 2.68%; when changing the design objective from maximum efficiency to maximum ecological objective function, the improvement of power output is 229.13%, and the efficiency drop is only 13.53%. - Highlights: • An irreversible single resonance energy selective electron heat engine is studied. • Heat leakage between two reservoirs is considered. • Power output, efficiency and ecological objective function are derived. • Optimal performance comparison for three objective functions is carried out.
Entropy-based financial asset pricing.
Directory of Open Access Journals (Sweden)
Mihály Ormos
Full Text Available We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.
Wavelet entropy characterization of elevated intracranial pressure.
Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao
2008-01-01
Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.
Entropy-based financial asset pricing.
Ormos, Mihály; Zibriczky, Dávid
2014-01-01
We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.
Investment Irreversibility and Precautionary Savings in General Equilibrium
DEFF Research Database (Denmark)
Ejarque, João
than irreversibility effects. If shocks are idiosyncratic and affect a cross section of agents over capital, an increase in their variance may induce an increase in aggregate investment even if all agents have an incentive to invest less, because zero investment is now an active lower bound for part...
The degree of irreversibility in deterministic finite automata
DEFF Research Database (Denmark)
Axelsen, Holger Bock; Holzer, Markus; Kutrib, Martin
2016-01-01
the language, and show that the degree induces a strict infinite hierarchy of languages. We examine how the degree of irreversibility behaves under the usual language operations union, intersection, complement, concatenation, and Kleene star, showing tight bounds (some asymptotically) on the degree....
Optimization at different loads by minimization of irreversibilities
International Nuclear Information System (INIS)
Wong, K.F.V.; Niu, Z.
1991-01-01
This paper reports that the irreversibility of the power cycle was chosen as the objective function as this function can successfully measure both the quality and quantity of energy flow in the cycle. Minimization of the irreversibility ensures that the power cycle will operate more efficiently. One feature of the present work is that the boiler, turbine, condenser and heaters are treated as one system for the purpose of optimization. In the optimization model, nine regression formulae are used, which are obtained from the measured test data. From the results of the present work, it can be seen that the optimization model developed can represent the effect of operational parameters on the power plant first and second law efficiency. Some of the results can be used to provide guidance for the optimal operation of the power plant. When the power cycle works at full load, the main steam temperature and pressure should be at the upper limit for minimal irreversibility of the system. If the load is less than 65% of its design capacity, the steam temperature and pressure should be decreased for a lower irreversibility of the system
Profit rate performance optimization for a generalized irreversible ...
Indian Academy of Sciences (India)
fer law system generalized irreversible combined refrigeration cycle model with finite-rate heat ...... Chen L, Sun F, Wu C 2004b Optimum allocation of heat exchanger area for refrigeration and air conditioning plants. Appl. Energy 77(3): 339– ...
Exergetic efficiency optimization for an irreversible heat pump ...
Indian Academy of Sciences (India)
This paper deals with the performance analysis and optimization for irreversible heat pumps working on reversed Brayton cycle with constant-temperature heat reservoirs by taking exergetic efficiency as the optimization objective combining exergy concept with finite-time thermodynamics (FTT). Exergetic efficiency is ...