Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics

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Pan Zhao

2018-01-01

Full Text Available In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model.

Non-extensive statistical aspects of clustering and nuclear multi-fragmentation

International Nuclear Information System (INIS)

Calboreanu, A.

2002-01-01

Recent developments concerning an application of the non-extensive Tsalis statistics to describe clustering phenomena is briefly presented. Cluster formation is a common feature of a large number of physical phenomena encountered in molecular and nuclear physics, astrophysics, condensed matter and biophysics. Common to all these is the large number of degrees of freedom, thus justifying a statistical approach. However the conventional statistical mechanics paradigm seems to fail in dealing with clustering. Whether this is due to the prevalence of complex dynamical constrains, or it is a manifestation of new statistics is a subject of considerable interest, which was intensively debated during the last few years. Tsalis conjecture has proved extremely appealing due to its rather elegant and transparent basic arguments. We present here evidence for its adequacy for the study of a large class of physical phenomena related to cluster formation. An application to nuclear multi-fragmentation is presented. (author)

Lattice QCD Thermodynamics and RHIC-BES Particle Production within Generic Nonextensive Statistics

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Tawfik, Abdel Nasser

2018-05-01

The current status of implementing Tsallis (nonextensive) statistics on high-energy physics is briefly reviewed. The remarkably low freezeout-temperature, which apparently fails to reproduce the firstprinciple lattice QCD thermodynamics and the measured particle ratios, etc. is discussed. The present work suggests a novel interpretation for the so-called " Tsallis-temperature". It is proposed that the low Tsallis-temperature is due to incomplete implementation of Tsallis algebra though exponential and logarithmic functions to the high-energy particle-production. Substituting Tsallis algebra into grand-canonical partition-function of the hadron resonance gas model seems not assuring full incorporation of nonextensivity or correlations in that model. The statistics describing the phase-space volume, the number of states and the possible changes in the elementary cells should be rather modified due to interacting correlated subsystems, of which the phase-space is consisting. Alternatively, two asymptotic properties, each is associated with a scaling function, are utilized to classify a generalized entropy for such a system with large ensemble (produced particles) and strong correlations. Both scaling exponents define equivalence classes for all interacting and noninteracting systems and unambiguously characterize any statistical system in its thermodynamic limit. We conclude that the nature of lattice QCD simulations is apparently extensive and accordingly the Boltzmann-Gibbs statistics is fully fulfilled. Furthermore, we found that the ratios of various particle yields at extreme high and extreme low energies of RHIC-BES is likely nonextensive but not necessarily of Tsallis type.

Keyword extraction by nonextensivity measure.

Science.gov (United States)

Mehri, Ali; Darooneh, Amir H

2011-05-01

The presence of a long-range correlation in the spatial distribution of a relevant word type, in spite of random occurrences of an irrelevant word type, is an important feature of human-written texts. We classify the correlation between the occurrences of words by nonextensive statistical mechanics for the word-ranking process. In particular, we look at the nonextensivity parameter as an alternative metric to measure the spatial correlation in the text, from which the words may be ranked in terms of this measure. Finally, we compare different methods for keyword extraction. © 2011 American Physical Society

Speed of Sound in Hadronic matter using Non-extensive Statistics

CERN Document Server

Khuntia, Arvind; Garg, Prakhar; Sahoo, Raghunath; Cleymans, Jean

2016-01-01

The speed of sound ($c_s$) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems, which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a function of temperature for different $q$-values for a hadron resonance gas. We observe a similar mass cut-off behaviour in non-extensive case for $c^{2}_s$ by including heavier particles, as is observed in the case of a hadron resonance gas following equilibrium statistics. Also, we explicitly present that the temperature where the mass cut-off starts, varies with the $q$-parameter which hints at a relation between the d...

Debye shielding in a nonextensive plasma

International Nuclear Information System (INIS)

Ait Gougam, Leila; Tribeche, Mouloud

2011-01-01

The phenomenon of Debye Shielding is revisited within the theoretical framework of the Tsallis statistical mechanics. The plasma consists of nonextensive electrons and ions. Both the effective Debye length λ D q and the fall-off of the electrostatic potential Φ are considered and a parameter study conducted. Owing to electron nonextensivity, the critical Mach number derived from the modified Bohm sheath criterion may become less than unity allowing therefore ions with speed less than ion-acoustic speed to enter the sheath from the main body of the plasma. Considering the wide relevance of collective processes, our analysis may be viewed as a first step toward a more comprehensive Debye shielding and electrostatic plasma sheath in nonequilibrium plasmas.

New exponential, logarithm and q-probability in the non-extensive statistical physics

OpenAIRE

Chung, Won Sang

2013-01-01

In this paper, a new exponential and logarithm related to the non-extensive statistical physics is proposed by using the q-sum and q-product which satisfy the distributivity. And we discuss the q-mapping from an ordinary probability to q-probability. The q-entropy defined by the idea of q-probability is shown to be q-additive.

Perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases.

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Mohammadzadeh, Hosein; Adli, Fereshteh; Nouri, Sahereh

2016-12-01

We investigate perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. We show that the intrinsic statistical interaction of nonextensive Bose (Fermi) gas is attractive (repulsive) similar to the extensive case but the value of thermodynamic curvature is changed by a nonextensive parameter. In contrary to the extensive ideal classical gas, the nonextensive one may be divided to two different regimes. According to the deviation parameter of the system to the nonextensive case, one can find a special value of fugacity, z^{*}, where the sign of thermodynamic curvature is changed. Therefore, we argue that the nonextensive parameter induces an attractive (repulsive) statistical interaction for zz^{*}) for an ideal classical gas. Also, according to the singular point of thermodynamic curvature, we consider the condensation of nonextensive Boson gas.

Dust ion-acoustic solitary waves in a dusty plasma with nonextensive electrons

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Bacha, Mustapha; Tribeche, Mouloud; Shukla, Padma Kant

2012-05-01

The dust-modified ion-acoustic waves of Shukla and Silin are revisited within the theoretical framework of the Tsallis statistical mechanics. Nonextensivity may originate from correlation or long-range plasma interactions. Interestingly, we find that owing to electron nonextensivity, dust ion-acoustic (DIA) solitary waves may exhibit either compression or rarefaction. Our analysis is then extended to include self-consistent dust charge fluctuation. In this connection, the correct nonextensive electron charging current is rederived. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, is obtained, making use of the reductive perturbation method. The DIA waves are then analyzed for parameters corresponding to space dusty plasma situations.

Speed of sound in hadronic matter using non-extensive Tsallis statistics

International Nuclear Information System (INIS)

Khuntia, Arvind; Sahoo, Pragati; Garg, Prakhar; Sahoo, Raghunath; Cleymans, Jean

2016-01-01

The speed of sound (c_s) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark-gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first-order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a function of temperature for different q-values for a hadron resonance gas. We observe a similar mass cut-off behaviour in the non-extensive case for c"2_s by including heavier particles, as is observed in the case of a hadron resonance gas following equilibrium statistics. Also, we explicitly show that the temperature where the mass cut-off starts varies with the q-parameter which hints at a relation between the degree of non-equilibrium and the limiting temperature of the system. It is shown that for values of q above approximately 1.13 all criticality disappears in the speed of sound, i.e. the decrease in the value of the speed of sound, observed at lower values of q, disappears completely. (orig.)

Speed of sound in hadronic matter using non-extensive Tsallis statistics

Energy Technology Data Exchange (ETDEWEB)

Khuntia, Arvind; Sahoo, Pragati; Garg, Prakhar; Sahoo, Raghunath [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Science, Simrol, M.P. (India); Cleymans, Jean [University of Cape Town, UCT-CERN Research Centre and Department of Physics, Rondebosch (South Africa)

2016-09-15

The speed of sound (c{sub s}) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark-gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first-order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a function of temperature for different q-values for a hadron resonance gas. We observe a similar mass cut-off behaviour in the non-extensive case for c{sup 2}{sub s} by including heavier particles, as is observed in the case of a hadron resonance gas following equilibrium statistics. Also, we explicitly show that the temperature where the mass cut-off starts varies with the q-parameter which hints at a relation between the degree of non-equilibrium and the limiting temperature of the system. It is shown that for values of q above approximately 1.13 all criticality disappears in the speed of sound, i.e. the decrease in the value of the speed of sound, observed at lower values of q, disappears completely. (orig.)

Non-Extensive Statistical Analysis of Magnetic Field and SEPs during the March 2012 ICME event, using a multi-spacecraft approach

Science.gov (United States)

Pavlos, George; Malandraki, Olga; Pavlos, Evgenios; Iliopoulos, Aggelos; Karakatsanis, Leonidas

2017-04-01

As the solar plasma lives far from equilibrium it is an excellent laboratory for testing non-equilibrium statistical mechanics. In this study, we present the highlights of Tsallis non-extensive statistical mechanics as concerns their applications at solar plasma dynamics, especially at solar wind phenomena and magnetosphere. In this study we present some new and significant results concerning the dynamics of interplanetary coronal mass ejections (ICMEs) observed in the near Earth at L1 solar wind environment, as well as its effect in Earth's magnetosphere. The results are referred to Tsallis non-extensive statistics and in particular to the estimation of Tsallis q-triplet, (qstat, qsen, qrel) of SEPs time series observed at the interplanetary space and magnetic field time series of the ICME observed at the Earth resulting from the solar eruptive activity on March 7, 2012 at the Sun. For the magnetic field, we used a multi-spacecraft approach based on data experiments from ACE, CLUSTER 4, THEMIS-E and THEMIS-C spacecraft. For the data analysis different time periods were considered, sorted as "quiet", "shock" and "aftershock", while different space domains such as the Interplanetary space (near Earth at L1 and upstream of the Earth's bowshock), the Earth's magnetosheath and magnetotail, were also taken into account. Our results reveal significant differences in statistical and dynamical features, indicating important variations of the SEPs profile in time, and magnetic field dynamics both in time and space domains during the shock event, in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states. So far, Tsallis non-extensive statistical theory and Tsallis extension of the Boltzmann-Gibbs entropy principle to the q-entropy entropy principle (Tsallis, 1988, 2009) reveal strong universality character concerning non-equilibrium dynamics (Pavlos et al. 2012a,b, 2014, 2015, 2016; Karakatsanis et al. 2013). Tsallis q

Non-Extensive Statistical Analysis of Solar Wind Electric, Magnetic Fields and Solar Energetic Particle time series.

Science.gov (United States)

Pavlos, G. P.; Malandraki, O.; Khabarova, O.; Livadiotis, G.; Pavlos, E.; Karakatsanis, L. P.; Iliopoulos, A. C.; Parisis, K.

2017-12-01

In this work we study the non-extensivity of Solar Wind space plasma by using electric-magnetic field data obtained by in situ spacecraft observations at different dynamical states of solar wind system especially in interplanetary coronal mass ejections (ICMEs), Interplanetary shocks, magnetic islands, or near the Earth Bow shock. Especially, we study the energetic particle non extensive fractional acceleration mechanism producing kappa distributions as well as the intermittent turbulence mechanism producing multifractal structures related with the Tsallis q-entropy principle. We present some new and significant results concerning the dynamics of ICMEs observed in the near Earth at L1 solar wind environment, as well as its effect in Earth's magnetosphere as well as magnetic islands. In-situ measurements of energetic particles at L1 are analyzed, in response to major solar eruptive events at the Sun (intense flares, fast CMEs). The statistical characteristics are obtained and compared for the Solar Energetic Particles (SEPs) originating at the Sun, the energetic particle enhancements associated with local acceleration during the CME-driven shock passage over the spacecraft (Energetic Particle Enhancements, ESPs) as well as the energetic particle signatures observed during the passage of the ICME. The results are referred to Tsallis non-extensive statistics and in particular to the estimation of Tsallis q-triplet, (qstat, qsen, qrel) of electric-magnetic field and the kappa distributions of solar energetic particles time series of the ICME, magnetic islands, resulting from the solar eruptive activity or the internal Solar Wind dynamics. Our results reveal significant differences in statistical and dynamical features, indicating important variations of the magnetic field dynamics both in time and space domains during the shock event, in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states.

Jeans' criterion and nonextensive velocity distribution function in kinetic theory

International Nuclear Information System (INIS)

Du Jiulin

2004-01-01

The effect of nonextensivity of self-gravitating systems on the Jeans' criterion for gravitational instability is studied in the framework of Tsallis statistics. The nonextensivity is introduced in the Jeans problem by a generalized q-nonextensive velocity distribution function through the equation of state of ideal gas in nonextensive kinetic theory. A new Jeans' criterion is deduced with a factor √(2/(5-3q)) that, however, differs from that one in [Astron. Astrophys. 396 (2002) 309] and new results of gravitational instability are analyzed for the nonextensive parameter q. An understanding of physical meaning of q and a possible seismic observation to find astronomical evidence for a value of q different from unity are also discussed

Azimuthal anisotropy in heavy-ion collisions using non-extensive statistics in Boltzmann transport equation

International Nuclear Information System (INIS)

Tripathy, S.; Tiwari, S.K.; Younus, M.; Sahoo, R.

2017-01-01

One of the major goals in heavy-ion physics is to understand the properties of Quark Gluon Plasma (QGP), a deconfined hot and dense state of quarks and gluons existed shortly after the Big Bang. In the present scenario, the high-energy particle accelerators are able to reach energies where this extremely dense nuclear matter can be probed for a short time. Here, we follow our earlier works which use non-extensive statistics in Boltzmann Transport Equation (BTE). We represent the initial distribution of particles with the help of Tsallis power law distribution parameterized by the nonextensive parameter q and the Tsallis temperature T, remembering the fact that their origin is due to hard scatterings. We use the initial distribution (f in ) with Relaxation Time Approximation (RTA) of the BTE and calculate the final distribution (f fin ). Then we calculate ν 2 of the system using the final distribution in the definition of ν2

A New Approach for the Statistical Thermodynamic Theory of the Nonextensive Systems Confined in Different Finite Traps

Science.gov (United States)

Tang, Hui-Yi; Wang, Jian-Hui; Ma, Yong-Li

2014-06-01

For a small system at a low temperature, thermal fluctuation and quantum effect play important roles in quantum thermodynamics. Starting from micro-canonical ensemble, we generalize the Boltzmann-Gibbs statistical factor from infinite to finite systems, no matter the interactions between particles are considered or not. This generalized factor, similar to Tsallis's q-form as a power-law distribution, has the restriction of finite energy spectrum and includes the nonextensivities of the small systems. We derive the exact expression for distribution of average particle numbers in the interacting classical and quantum nonextensive systems within a generalized canonical ensemble. This expression in the almost independent or elementary excitation quantum finite systems is similar to the corresponding ones obtained from the conventional grand-canonical ensemble. In the reconstruction for the statistical theory of the small systems, we present the entropy of the equilibrium systems and equation of total thermal energy. When we investigate the thermodynamics for the interacting nonextensive systems, we obtain the system-bath heat exchange and "uncompensated heat" which are in the thermodynamical level and independent on the detail of the system-bath coupling. For ideal finite systems, with different traps and boundary conditions, we calculate some thermodynamic quantities, such as the specific heat, entropy, and equation of state, etc. Particularly at low temperatures for the small systems, we predict some novel behaviors in the quantum thermodynamics, including internal entropy production, heat exchanges between the system and its surroundings and finite-size effects on the free energy.

ΛCDM model with dissipative nonextensive viscous dark matter

Science.gov (United States)

Gimenes, H. S.; Viswanathan, G. M.; Silva, R.

2018-03-01

Many models in cosmology typically assume the standard bulk viscosity. We study an alternative interpretation for the origin of the bulk viscosity. Using nonadditive statistics proposed by Tsallis, we propose a bulk viscosity component that can only exist by a nonextensive effect through the nonextensive/dissipative correspondence (NexDC). In this paper, we consider a ΛCDM model for a flat universe with a dissipative nonextensive viscous dark matter component, following the Eckart theory of bulk viscosity, without any perturbative approach. In order to analyze cosmological constraints, we use one of the most recent observations of Type Ia Supernova, baryon acoustic oscillations and cosmic microwave background data.

Non-extensive Statistics to the Cosmological Lithium Problem

Science.gov (United States)

Hou, S. Q.; He, J. J.; Parikh, A.; Kahl, D.; Bertulani, C. A.; Kajino, T.; Mathews, G. J.; Zhao, G.

2017-01-01

Big Bang nucleosynthesis (BBN) theory predicts the abundances of the light elements D, 3He, 4He, and 7Li produced in the early universe. The primordial abundances of D and 4He inferred from observational data are in good agreement with predictions, however, BBN theory overestimates the primordial 7Li abundance by about a factor of three. This is the so-called “cosmological lithium problem.” Solutions to this problem using conventional astrophysics and nuclear physics have not been successful over the past few decades, probably indicating the presence of new physics during the era of BBN. We have investigated the impact on BBN predictions of adopting a generalized distribution to describe the velocities of nucleons in the framework of Tsallis non-extensive statistics. This generalized velocity distribution is characterized by a parameter q, and reduces to the usually assumed Maxwell-Boltzmann distribution for q = 1. We find excellent agreement between predicted and observed primordial abundances of D, 4He, and 7Li for 1.069 ≤ q ≤ 1.082, suggesting a possible new solution to the cosmological lithium problem.

Speed of sound in hadronic matter using non-extensive statistics

International Nuclear Information System (INIS)

Khuntia, Arvind; Sahoo, Pragati; Garg, Prakhar; Sahoo, Raghunath; Jean Cleymans

2015-01-01

The evolution of the dense matter formed in high energy hadronic and nuclear collisions is controlled by the initial energy density and temperature. The expansion of the system is due to the very high initial pressure with lowering of temperature and energy density. The pressure (P) and energy density (ϵ) are related through speed of sound (c 2 s ) under the condition of local thermal equilibrium. The speed of sound plays a crucial role in hydrodynamical expansion of the dense matter created and the critical behaviour of the system evolving from deconfined Quark Gluon Phase (QGP) to confined hadronic phase. There have been several experimental and theoretical studies in this direction. The non-extensive Tsallis statistics gives better description of the transverse momentum spectra of the produced particles created in high energy p + p (p¯) and e + + e - collisions

Applying incomplete statistics to nonextensive systems with different q indices

International Nuclear Information System (INIS)

Nivanen, L.; Pezeril, M.; Wang, Q.A.; Mehaute, A. Le

2005-01-01

The nonextensive statistics based on the q-entropy Sq=--bar i=1v(pi-piq)1-q has been so far applied to systems in which the q value is uniformly distributed. For the systems containing different q's, the applicability of the theory is still a matter of investigation. The difficulty is that the class of systems to which the theory can be applied is actually limited by the usual nonadditivity rule of entropy which is no more valid when the systems contain non uniform distribution of q values. In this paper, within the framework of the so called incomplete information theory, we propose a more general nonadditivity rule of entropy prescribed by the zeroth law of thermodynamics. This new nonadditivity generalizes in a simple way the usual one and can be proved to lead uniquely to the q-entropy

Phase transition for the system of finite volume in the ϕ4 theory in the Tsallis nonextensive statistics

Science.gov (United States)

Ishihara, Masamichi

2018-04-01

We studied the effects of nonextensivity on the phase transition for the system of finite volume V in the ϕ4 theory in the Tsallis nonextensive statistics of entropic parameter q and temperature T, when the deviation from the Boltzmann-Gibbs (BG) statistics, |q ‑ 1|, is small. We calculated the condensate and the effective mass to the order q ‑ 1 with the normalized q-expectation value under the free particle approximation with zero bare mass. The following facts were found. The condensate Φ divided by v, Φ/v, at q (v is the value of the condensate at T = 0) is smaller than that at q‧ for q > q‧ as a function of Tph/v which is the physical temperature Tph divided by v. The physical temperature Tph is related to the variation of the Tsallis entropy and the variation of the internal energies, and Tph at q = 1 coincides with T. The effective mass decreases, reaches minimum, and increases after that, as Tph increases. The effective mass at q > 1 is lighter than the effective mass at q = 1 at low physical temperature and heavier than the effective mass at q = 1 at high physical temperature. The effects of the nonextensivity on the physical quantity as a function of Tph become strong as |q ‑ 1| increases. The results indicate the significance of the definition of the expectation value, the definition of the physical temperature, and the constraints for the density operator, when the terms including the volume of the system are not negligible.

NON-EXTENSIVE STATISTICS TO THE COSMOLOGICAL LITHIUM PROBLEM

Energy Technology Data Exchange (ETDEWEB)

Hou, S. Q.; He, J. J. [Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China); Parikh, A. [Departament de Física i Enginyeria Nuclear, EUETIB, Universitat Politècnica de Catalunya, Barcelona E-08036 (Spain); Kahl, D. [Center for Nuclear Study, The University of Tokyo, RIKEN campus, Wako, Saitama 351-0198 (Japan); Bertulani, C. A. [Texas A and M University-Commerce, Commerce, TX 75429-3011 (United States); Kajino, T. [Department of Astronomy, School of Science, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan); Mathews, G. J. [National Astronomical Observatory of Japan 2-21-1 Osawa, Mitaka, Tokyo, 181-8588 (Japan); Zhao, G., E-mail: hejianjun@nao.cas.cn [Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China)

2017-01-10

Big Bang nucleosynthesis (BBN) theory predicts the abundances of the light elements D, {sup 3}He, {sup 4}He, and {sup 7}Li produced in the early universe. The primordial abundances of D and {sup 4}He inferred from observational data are in good agreement with predictions, however, BBN theory overestimates the primordial {sup 7}Li abundance by about a factor of three. This is the so-called “cosmological lithium problem.” Solutions to this problem using conventional astrophysics and nuclear physics have not been successful over the past few decades, probably indicating the presence of new physics during the era of BBN. We have investigated the impact on BBN predictions of adopting a generalized distribution to describe the velocities of nucleons in the framework of Tsallis non-extensive statistics. This generalized velocity distribution is characterized by a parameter q , and reduces to the usually assumed Maxwell–Boltzmann distribution for q  = 1. We find excellent agreement between predicted and observed primordial abundances of D, {sup 4}He, and {sup 7}Li for 1.069 ≤  q  ≤ 1.082, suggesting a possible new solution to the cosmological lithium problem.

Statistical mechanics and the description of the early universe I

DEFF Research Database (Denmark)

Pessah, Martin Elias; F. Torres, Diego; Vucetich, H.

2001-01-01

We analyze how the thermal history of the universe is influenced by the statistical description, assuming a deviation from the usual Bose-Einstein, Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations represent the possible appearance of non-extensive effects related with the ......We analyze how the thermal history of the universe is influenced by the statistical description, assuming a deviation from the usual Bose-Einstein, Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations represent the possible appearance of non-extensive effects related...... and to place limits to the range of its validity. The corrections obtained will change with temperature, and consequently, the bounds on the possible amount of non-extensivity will also change with time. We generalize results which can be used in other contexts as well, as the Boltzmann equation and the Saha...

Systematic Analysis of the Non-Extensive Statistical Approach in High Energy Particle Collisions—Experiment vs. Theory †

Directory of Open Access Journals (Sweden)

Gábor Bíró

2017-02-01

Full Text Available The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or nuclear collisions, the number of particles is several orders of magnitude smaller than the Avogadro number; therefore, finite-size and fluctuation effects strongly influence the final-state one-particle energy distributions. Due to the simple characterization, the description of the identified hadron spectra with the Boltzmann–Gibbs thermodynamical approach is insufficient. These spectra can be described very well with Tsallis–Pareto distributions instead, derived from non-extensive thermodynamics. Using the q-entropy formula, we interpret the microscopic physics in terms of the Tsallis q and T parameters. In this paper we give a view on these parameters, analyzing identified hadron spectra from recent years in a wide center-of-mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on the center-of-mass energy and particle species (mass. Our findings are described well by a QCD (Quantum Chromodynamics inspired parton evolution ansatz. Based on this comprehensive study, apart from the evolution, both mesonic and baryonic components found to be non-extensive ( q > 1 , besides the mass ordered hierarchy observed in the parameter T. We also study and compare in details the theory-obtained parameters for the case of PYTHIA8 Monte Carlo Generator, perturbative QCD and quark coalescence models.

Nonextensive Thomas-Fermi model

Science.gov (United States)

Shivamoggi, Bhimsen; Martinenko, Evgeny

2007-11-01

Nonextensive Thomas-Fermi model was father investigated in the following directions: Heavy atom in strong magnetic field. following Shivamoggi work on the extension of Kadomtsev equation we applied nonextensive formalism to father generalize TF model for the very strong magnetic fields (of order 10e12 G). The generalized TF equation and the binding energy of atom were calculated which contain a new nonextensive term dominating the classical one. The binding energy of a heavy atom was also evaluated. Thomas-Fermi equations in N dimensions which is technically the same as in Shivamoggi (1998) ,but behavior is different and in interesting 2 D case nonextesivity prevents from becoming linear ODE as in classical case. Effect of nonextensivity on dielectrical screening reveals itself in the reduction of the envelope radius. It was shown that nonextesivity in each case is responsible for new term dominating classical thermal correction term by order of magnitude, which is vanishing in a limit q->1. Therefore it appears that nonextensive term is ubiquitous for a wide range of systems and father work is needed to understand the origin of it.

Nonextensive electron and ion dust charging currents

International Nuclear Information System (INIS)

Amour, Rabia; Tribeche, Mouloud

2011-01-01

The correct nonextensive electron and ion charging currents are presented for the first time based on the orbit motion limited approach. For -1< q<1, where q measures the amount of plasma nonextensivity, the nonextensive electron charging current is expressed in terms of the hypergeometric function. The variable dust charge is expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate succinctly the effects of nonextensive charge carriers. The obtained formulas bring a possibility to build theories on nonlinear collective process in variable charge nonextensive dusty plasmas.

The nonextensive gas: a kinetic approach

International Nuclear Information System (INIS)

Lima, J.A.S.; Silva, R.

2005-01-01

We discuss a kinetic nonextensive generalization of the Maxwellian ideal gas. The analysis rests on two basic assumptions: (i) instead of the standard Gaussian form, the q-gas is described by a power-law velocity distribution as suggested in the nonextensive Tsallis' framework (ii) the q-nonextensive generalization of the Boltzmann entropy formula governs the behavior of the q-gas. In this context, we show that the pressure and the internal energy are kinetically modified, but the general equation of state, PV=2U/3, remains valid. The adiabatic index is now a function of the nonextensive parameter, γ=C p /C V =5/3q. However, the standard expression relating the specific heats (at constant pressure and volume) with the coefficient of expansion and the isothermal compressibility, C P -C V =TVα 2 /κ T , is not modified

Variable charge dust acoustic solitary waves in a dusty plasma with a q-nonextensive electron velocity distribution

International Nuclear Information System (INIS)

Amour, Rabia; Tribeche, Mouloud

2010-01-01

A first theoretical work is presented to study variable charge dust acoustic solitons within the theoretical framework of the Tsallis statistical mechanics. Our results reveal that the spatial patterns of the variable charge solitary wave are significantly modified by electron nonextensive effects. In particular, it may be noted that for -1 d becomes more negative and the dust grains localization (accumulation) less pronounced. The electrons are locally expelled and pushed out of the region of the soliton's localization. This electron depletion becomes less effective as the electrons evolve far away from their thermal equilibrium. The case q>1 provides qualitatively opposite results: electron nonextensivity makes the solitary structure more spiky. Our results should help in providing a good fit between theoretical and experimental results.

Generalized statistical mechanics approaches to earthquakes and tectonics

Science.gov (United States)

Papadakis, Giorgos; Michas, Georgios

2016-01-01

Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed. The scale-invariant properties, the (multi) fractal structures and the long-range interactions that have been found to characterize fault and earthquake populations have recently led to the consideration of non-extensive statistical mechanics (NESM) as a consistent statistical mechanics framework for the description of seismicity. The consistency between NESM and observations has been demonstrated in a series of publications on seismicity, faulting, rock physics and other fields of geosciences. The aim of this review is to present in a concise manner the fundamental macroscopic properties of earthquakes and faulting and how these can be derived by using the notions of statistical mechanics and NESM, providing further insights into earthquake physics and fault growth processes. PMID:28119548

Application of the non-extensive statistical approach to high energy particle collisions

Science.gov (United States)

Bíró, Gábor; Barnaföldi, Gergely Gábor; Biró, Tamás Sándor; Ürmössy, Károly

2017-06-01

In high-energy collisions the number of created particles is far less than the thermodynamic limit, especially in small colliding systems (e.g. proton-proton). Therefore final-state effects and fluctuations in the one-particle energy distribution are appreciable. As a consequence the characterization of identified hadron spectra with the Boltzmann - Gibbs thermodynamical approach is insuffcient [1]. Instead particle spectra measured in high-energy collisions can be described very well with Tsallis -Pareto distributions, derived from non-extensive thermodynamics [2, 3]. Using the Tsallis q-entropy formula, a generalization of the Boltzmann - Gibbs entropy, we interpret the microscopic physics by analysing the Tsallis q and T parameters. In this paper we give a quick overview on these parameters, analyzing identified hadron spectra from recent years in a wide center-of-mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on the center-of-mass energy and particle species. Our findings are described well by a QCD inspired evolution ansatz. Based on this comprehensive study, apart from the evolution, both mesonic and barionic components found to be non-extensive (q > 1), beside the mass ordered hierarchy observed in parameter T.

On non-extensive nature of thermal conductivity

Indian Academy of Sciences (India)

Abstract. In this paper we study non-extensive nature of thermal conductivity. It is observed that there is similarity between non-extensive entropic index and fractal dimension obtained for the silica aerogel thermal conductivity data at low temperature.

Worldwide seismicity in view of non-extensive statistical physics

Science.gov (United States)

Chochlaki, Kaliopi; Vallianatos, Filippos; Michas, George

2014-05-01

In the present work we study the distribution of worldwide shallow seismic events occurred from 1981 to 2011 extracted from the CMT catalog, with magnitude equal or greater than Mw 5.0. Our analysis based on the subdivision of the Earth surface into seismic zones that are homogeneous with regards to seismic activity and orientation of the predominant stress field. To this direction we use the Flinn-Engdahl regionalization (Flinn and Engdahl, 1965), which consists of 50 seismic zones as modified by Lombardi and Marzocchi (2007), where grouped the 50 FE zones into larger tectonically homogeneous ones, utilizing the cumulative moment tensor method. As a result Lombardi and Marzocchi (2007), limit the initial 50 regions to 39 ones, in which we apply the non- extensive statistical physics approach. The non-extensive statistical physics seems to be the most adequate and promising methodological tool for analyzing complex systems, such as the Earth's interior. In this frame, we introduce the q-exponential formulation as the expression of probability distribution function that maximizes the Sq entropy as defined by Tsallis, (1988). In the present work we analyze the interevent time distribution between successive earthquakes by a q-exponential function in each of the seismic zones defined by Lombardi and Marzocchi (2007).confirming the importance of long-range interactions and the existence of a power-law approximation in the distribution of the interevent times. Our findings supports the ideas of universality within the Tsallis approach to describe Earth's seismicity and present strong evidence on temporal clustering of seismic activity in each of the tectonic zones analyzed. Our analysis as applied in worldwide seismicity with magnitude equal or greater than Mw 5.5 and 6.) is presented and the dependence of our result on the cut-off magnitude is discussed. This research has been funded by the European Union (European Social Fund) and Greek national resources under the

Asymmetry of price returns-Analysis and perspectives from a non-extensive statistical physics point of view.

Directory of Open Access Journals (Sweden)

Łukasz Bil

Full Text Available We study how the approach grounded on non-extensive statistical physics can be applied to describe and distinguish different stages of the stock and money market development. A particular attention is given to asymmetric behavior of fat tailed distributions of positive and negative returns. A new method to measure this asymmetry is proposed. It is based on the value of the non-extensive Tsallis parameter q. The new quantifier of the relative asymmetry level between tails in terms of the Tsallis parameters q± is provided to analyze the effect of memory in data caused by nonlinear autocorrelations. The presented analysis takes into account data of separate stocks from the main developing stock market in Europe, i.e., the Warsaw Stock Exchange (WSE in Poland and-for comparison-data from the most mature money market (Forex. It is argued that the proposed new quantifier is able to describe the stage of market development and its robustness to speculation. The main strength is put on a description and interpretation of the asymmetry between statistical properties of positive and negative returns for various stocks and for diversified time-lags Δt of data counting. The particular caution in this context is addressed to the difference between intraday and interday returns. Our search is extended to study memory effects and their dependence on the quotation frequency for similar large companies-owners of food-industrial retail supermarkets acting on both Polish and European markets (Eurocash, Jeronimo-Martins, Carrefour, Tesco-but traded on various European stock markets of diversified economical maturity (respectively in Warsaw, Lisbon, Paris and London. The latter analysis seems to indicate quantitatively that stocks from the same economic sector traded on different markets within European Union (EU may be a target of diversified level of speculations involved in trading independently on the true economic situation of the company. Our work thus gives

Asymmetry of price returns—Analysis and perspectives from a non-extensive statistical physics point of view

Science.gov (United States)

Bil, Łukasz; Zienowicz, Magdalena

2017-01-01

We study how the approach grounded on non-extensive statistical physics can be applied to describe and distinguish different stages of the stock and money market development. A particular attention is given to asymmetric behavior of fat tailed distributions of positive and negative returns. A new method to measure this asymmetry is proposed. It is based on the value of the non-extensive Tsallis parameter q. The new quantifier of the relative asymmetry level between tails in terms of the Tsallis parameters q± is provided to analyze the effect of memory in data caused by nonlinear autocorrelations. The presented analysis takes into account data of separate stocks from the main developing stock market in Europe, i.e., the Warsaw Stock Exchange (WSE) in Poland and—for comparison—data from the most mature money market (Forex). It is argued that the proposed new quantifier is able to describe the stage of market development and its robustness to speculation. The main strength is put on a description and interpretation of the asymmetry between statistical properties of positive and negative returns for various stocks and for diversified time-lags Δt of data counting. The particular caution in this context is addressed to the difference between intraday and interday returns. Our search is extended to study memory effects and their dependence on the quotation frequency for similar large companies—owners of food-industrial retail supermarkets acting on both Polish and European markets (Eurocash, Jeronimo-Martins, Carrefour, Tesco)—but traded on various European stock markets of diversified economical maturity (respectively in Warsaw, Lisbon, Paris and London). The latter analysis seems to indicate quantitatively that stocks from the same economic sector traded on different markets within European Union (EU) may be a target of diversified level of speculations involved in trading independently on the true economic situation of the company. Our work thus gives

Asymmetry of price returns-Analysis and perspectives from a non-extensive statistical physics point of view.

Science.gov (United States)

Bil, Łukasz; Grech, Dariusz; Zienowicz, Magdalena

2017-01-01

We study how the approach grounded on non-extensive statistical physics can be applied to describe and distinguish different stages of the stock and money market development. A particular attention is given to asymmetric behavior of fat tailed distributions of positive and negative returns. A new method to measure this asymmetry is proposed. It is based on the value of the non-extensive Tsallis parameter q. The new quantifier of the relative asymmetry level between tails in terms of the Tsallis parameters q± is provided to analyze the effect of memory in data caused by nonlinear autocorrelations. The presented analysis takes into account data of separate stocks from the main developing stock market in Europe, i.e., the Warsaw Stock Exchange (WSE) in Poland and-for comparison-data from the most mature money market (Forex). It is argued that the proposed new quantifier is able to describe the stage of market development and its robustness to speculation. The main strength is put on a description and interpretation of the asymmetry between statistical properties of positive and negative returns for various stocks and for diversified time-lags Δt of data counting. The particular caution in this context is addressed to the difference between intraday and interday returns. Our search is extended to study memory effects and their dependence on the quotation frequency for similar large companies-owners of food-industrial retail supermarkets acting on both Polish and European markets (Eurocash, Jeronimo-Martins, Carrefour, Tesco)-but traded on various European stock markets of diversified economical maturity (respectively in Warsaw, Lisbon, Paris and London). The latter analysis seems to indicate quantitatively that stocks from the same economic sector traded on different markets within European Union (EU) may be a target of diversified level of speculations involved in trading independently on the true economic situation of the company. Our work thus gives indications

Evidence of Non-extensivity in Earth's Ambient Noise

Science.gov (United States)

Koutalonis, Ioannis; Vallianatos, Filippos

2017-12-01

The study of ambient seismic noise is one of the important scientific and practical research challenges, due to its use in a number of geophysical applications. In this work, we describe Earth's ambient noise fluctuations in terms of non-extensive statistical physics. We found that Earth's ambient noise increments follow the q-Gaussian distribution. This indicates that Earth's ambient noise's fluctuations are not random and present long-term memory effects that could be described in terms of Tsallis entropy. Our results suggest that q values depend on the time length used and that the non-extensive parameter, q, converges to value q → 1 for short-time windows and a saturation value of q ≈ 1.33 for longer ones. The results are discussed from the point of view of superstatistics introduced by Beck [Contin Mech Thermodyn 16(3):293-304, 2004] and connects the q values with the system's degrees of freedom. Our work indicates that the converged (maximum) value is q = 1.33 and is related to 5 degrees of freedom.

Debye shielding in a dusty plasma with nonextensively distributed electrons and ions

International Nuclear Information System (INIS)

Liu, Y.; Xu, K.; Liu, S. Q.

2012-01-01

The phenomenon of Debye shielding in dusty plasmas is investigated within the framework of nonextensively distributed electrons and ions. The effects of dust grain charge fluctuation are considered. It shows that the increase of the nonextensive parameters of electrons and ions will lead to the decrease of the shielding distance and it is due to that the effective temperature of nonextensively distributed particles drops with the increase of nonextensive parameters. There is a rather interesting result that the Debye shielding effects may vanish in a certain condition when the fluctuation of the dust grain charges is taken into account.

Complexity, Metastability and Nonextensivity

Science.gov (United States)

Beck, C.; Benedek, G.; Rapisarda, A.; Tsallis, C.

Work and heat fluctuations in systems with deterministic and stochastic forces / E. G. D. Cohen and R. Van Zon -- Is the entropy S[symbol] extensive or nonextensive? / C. Tsallis -- Superstatistics: recent developments and applications / C. Beck -- Two stories outside Boltzmann-Gibbs statistics: Mori's Q-phase transitions and glassy dynamics at the onset of chaos / A. Robledo, F. Baldovin and E. Mayoral -- Time-averages and the heat theorem / A. Carati -- Fundamental formulae and numerical evidences for the central limit theorem in Tsallis statistics / H. Suyari -- Generalizing the Planck distribution / A. M. C. Soma and C. Tsallis -- The physical roots of complexity: renewal or modulation? / P. Grigolini -- Nonequivalent ensembles and metastability / H. Touchette and R. S. Ellis -- Statistical physics for cosmic structures / L. Pietronero and F. Sylos Labini -- Metastability and anomalous behavior in the HMF model: connections to nonextensive thermodynamics and glassy dynamics / A. Pluchino, A. Rapisarda and V. Latora -- Vlasov analysis of relaxation and meta-equilibrium / C. Anteneodo and R. O. Vallejos -- Weak chaos in large conservative systems - infinite-range coupled standard maps / L. G. Moyano, A. P. Majtey and C. Tsallis -- Deterministc aging / E. Barkai -- Edge of chaos of the classical kicked top map: sensitivity to initial conditions / S. M. Duarte Queirós and C. Tsallis -- What entropy at the edge of chaos? / M. Lissia, M. Coraddu and R. Tonelli -- Fractal growth of carbon schwarzites / G. Benedek ... [et al.] -- Clustering and interface propagation in interacting particle dynamics / A. Provata and V. K. Noussiou -- Resonant activation and noise enhanced stability in Josephson junctions / A. L. Pankratov and B. Spagnolo -- Symmetry breaking induced directed motions / C.-H. Chang and T. Y. Tsong -- General theory of Galilean-invariant entropic lattic Boltzmann models / B. M. Boghosian -- Unifying approach to the jamming transition in granular media and

TIME-DEPENDENT NONEXTENSIVITY ARISING FROM THE ROTATIONAL EVOLUTION OF SOLAR-TYPE STARS

Energy Technology Data Exchange (ETDEWEB)

Silva, J. R. P.; Nepomuceno, M. M. F.; Soares, B. B.; De Freitas, D. B., E-mail: joseronaldo@uern.br [Departamento de Física, Universidade do Estado do Rio Grande do Norte, Mossoró-RN (Brazil)

2013-11-01

Nonextensive formalism is a generalization of the Boltzmann-Gibbs statistics. In this formalism, the entropic index q is a quantity characterizing the degree of nonextensivity and is interpreted as a parameter of long-memory or long-range interactions between the components of the system. Since its proposition in 1988, this formalism has been applied to investigate a wide variety of natural phenomena. In stellar astrophysics, a theoretical distribution function based on nonextensive formalism (q distributions) has been successfully applied to reproduce the distribution of stellar radial and rotational velocity data. In this paper, we investigate the time variation of the entropic index q obtained from the distribution of rotation, Vsin i, for a sample of 254 rotational data for solar-type stars from 11 open clusters aged between 35.5 Myr and 2.6 Gyr. As a result, we have found an anti-correlation between the entropic index q and the age of clusters, and that the distribution of rotation Vsin i for these stars becomes extensive for an age greater than about 170 Myr. Assuming that the parameter q is associated with long-memory effects, we suggest that the memory of the initial angular momentum of solar-type stars can be scaled by the entropic index q. We also propose a physical link between the parameter q and the magnetic braking of stellar rotation.

Nonextensive dust acoustic waves in a charge varying dusty plasma

Science.gov (United States)

Bacha, Mustapha; Tribeche, Mouloud

2012-01-01

Our recent analysis on nonlinear nonextensive dust-acoustic waves (DA) [Amour and Tribeche in Phys. Plasmas 17:063702, 2010] is extended to include self-consistent nonadiabatic grain charge fluctuation. The appropriate nonextensive electron charging current is rederived based on the orbit-limited motion theory. Our results reveal that the amplitude, strength and nature of the nonlinear DA waves (solitons and shocks) are extremely sensitive to the degree of ion nonextensivity. Stronger is the electron correlation, more important is the charge variation induced nonlinear wave damping. The anomalous dissipation effects may prevail over that dispersion as the electrons evolve far away from their Maxwellian equilibrium. Our investigation may be of wide relevance to astronomers and space scientists working on interstellar dusty plasmas where nonthermal distributions are turning out to be a very common and characteristic feature.

Nonextensive GES instability with nonlinear pressure effects

Directory of Open Access Journals (Sweden)

Munmi Gohain

2018-03-01

Full Text Available We herein analyze the instability dynamics associated with the nonextensive nonthermal gravito-electrostatic sheath (GES model for the perturbed solar plasma portraiture. The usual neutral gas approximation is herewith judiciously relaxed and the laboratory plasma-wall interaction physics is procedurally incorporated amid barotropic nonlinearity. The main motivation here stems from the true nature of the solar plasma system as a set of concentric nonlocal nonthermal sub-layers as evidenced from different multi-space satellite probes and missions. The formalism couples the solar interior plasma (SIP, bounded and solar wind plasma (SWP, unbounded via the diffused solar surface boundary (SSB formed due to an exact long-range gravito-electrostatic force-equilibration. A linear normal mode ansatz reveals both dispersive and non-dispersive features of the modified GES collective wave excitations. It is seen that the thermostatistical GES stability depends solely on the electron-to-ion temperature ratio. The damping behavior on both the scales is more pronounced in the acoustic domain, K→∞, than the gravitational domain, K→0; where, K is the Jeans-normalized angular wave number. It offers a unique quasi-linear coupling of the gravitational and acoustic fluctuations amid the GES force action. The results may be useful to see the excitation dynamics of natural normal modes in bounded nonextensive astero-environs from a new viewpoint of the plasma-wall coupling mechanism.

Nonextensive GES instability with nonlinear pressure effects

Science.gov (United States)

Gohain, Munmi; Karmakar, Pralay Kumar

2018-03-01

We herein analyze the instability dynamics associated with the nonextensive nonthermal gravito-electrostatic sheath (GES) model for the perturbed solar plasma portraiture. The usual neutral gas approximation is herewith judiciously relaxed and the laboratory plasma-wall interaction physics is procedurally incorporated amid barotropic nonlinearity. The main motivation here stems from the true nature of the solar plasma system as a set of concentric nonlocal nonthermal sub-layers as evidenced from different multi-space satellite probes and missions. The formalism couples the solar interior plasma (SIP, bounded) and solar wind plasma (SWP, unbounded) via the diffused solar surface boundary (SSB) formed due to an exact long-range gravito-electrostatic force-equilibration. A linear normal mode ansatz reveals both dispersive and non-dispersive features of the modified GES collective wave excitations. It is seen that the thermostatistical GES stability depends solely on the electron-to-ion temperature ratio. The damping behavior on both the scales is more pronounced in the acoustic domain, K → ∞ , than the gravitational domain, K → 0 ; where, K is the Jeans-normalized angular wave number. It offers a unique quasi-linear coupling of the gravitational and acoustic fluctuations amid the GES force action. The results may be useful to see the excitation dynamics of natural normal modes in bounded nonextensive astero-environs from a new viewpoint of the plasma-wall coupling mechanism.

An example of the interplay of nonextensivity and dynamics in the description of QCD matter

Energy Technology Data Exchange (ETDEWEB)

Rozynek, Jacek; Wilk, Grzegorz [National Centre for Nuclear Research, Department of Fundamental Research, Warsaw (Poland)

2016-09-15

Using a simple quasiparticle model of QCD matter, presented some time ago in the literature, in which interactions are modelled by some effective fugacities z, we investigate the interplay between the dynamical content of fugacities z and effects induced by nonextensivity in situations when this model is used in a nonextensive environment characterized by some nonextensive parameter q ≠ 1 (for the usual extensive case q = 1). This allows for a better understanding of the role of nonextensivity in the more complicated descriptions of dense hadronic and QCD matter recently presented (in which dynamics is defined by a Lagrangian, the form of which is specific to a given model). (orig.)

Global regionalized seismicity in view of Non-Extensive Statistical Physics

Science.gov (United States)

Chochlaki, Kalliopi; Vallianatos, Filippos; Michas, Georgios

2018-03-01

In the present work we study the distribution of Earth's shallow seismicity on different seismic zones, as occurred from 1981 to 2011 and extracted from the Centroid Moment Tensor (CMT) catalog. Our analysis is based on the subdivision of the Earth's surface into seismic zones that are homogeneous with regards to seismic activity and orientation of the predominant stress field. For this, we use the Flinn-Engdahl regionalization (FE) (Flinn and Engdahl, 1965), which consists of fifty seismic zones as modified by Lombardi and Marzocchi (2007). The latter authors grouped the 50 FE zones into larger tectonically homogeneous ones, utilizing the cumulative moment tensor method, resulting into thirty-nine seismic zones. In each one of these seismic zones we study the distribution of seismicity in terms of the frequency-magnitude distribution and the inter-event time distribution between successive earthquakes, a task that is essential for hazard assessments and to better understand the global and regional geodynamics. In our analysis we use non-extensive statistical physics (NESP), which seems to be one of the most adequate and promising methodological tools for analyzing complex systems, such as the Earth's seismicity, introducing the q-exponential formulation as the expression of probability distribution function that maximizes the Sq entropy as defined by Tsallis, (1988). The qE parameter is significantly greater than one for all the seismic regions analyzed with value range from 1.294 to 1.504, indicating that magnitude correlations are particularly strong. Furthermore, the qT parameter shows some temporal correlations but variations with cut-off magnitude show greater temporal correlations when the smaller magnitude earthquakes are included. The qT for earthquakes with magnitude greater than 5 takes values from 1.043 to 1.353 and as we increase the cut-off magnitude to 5.5 and 6 the qT value ranges from 1.001 to 1.242 and from 1.001 to 1.181 respectively, presenting

Comparing emerging and mature markets during times of crises: A non-extensive statistical approach

Science.gov (United States)

Namaki, A.; Koohi Lai, Z.; Jafari, G. R.; Raei, R.; Tehrani, R.

2013-07-01

One of the important issues in finance and economics for both scholars and practitioners is to describe the behavior of markets, especially during times of crises. In this paper, we analyze the behavior of some mature and emerging markets with a Tsallis entropy framework that is a non-extensive statistical approach based on non-linear dynamics. During the past decade, this technique has been successfully applied to a considerable number of complex systems such as stock markets in order to describe the non-Gaussian behavior of these systems. In this approach, there is a parameter q, which is a measure of deviation from Gaussianity, that has proved to be a good index for detecting crises. We investigate the behavior of this parameter in different time scales for the market indices. It could be seen that the specified pattern for q differs for mature markets with regard to emerging markets. The findings show the robustness of the stated approach in order to follow the market conditions over time. It is obvious that, in times of crises, q is much greater than in other times. In addition, the response of emerging markets to global events is delayed compared to that of mature markets, and tends to a Gaussian profile on increasing the scale. This approach could be very useful in application to risk and portfolio management in order to detect crises by following the parameter q in different time scales.

Nuclear multifragmentation, its relation to general physics. A rich test ground of the fundamentals of statistical mechanics

International Nuclear Information System (INIS)

Gross, D.H.E.

2006-01-01

Heat can flow from cold to hot at any phase separation even in macroscopic systems. Therefore also Lynden-Bell's famous gravo-thermal catastrophe must be reconsidered. In contrast to traditional canonical Boltzmann-Gibbs statistics this is correctly described only by microcanonical statistics. Systems studied in chemical thermodynamics (ChTh) by using canonical statistics consist of several homogeneous macroscopic phases. Evidently, macroscopic statistics as in chemistry cannot and should not be applied to non-extensive or inhomogeneous systems like nuclei or galaxies. Nuclei are small and inhomogeneous. Multifragmented nuclei are even more inhomogeneous and the fragments even smaller. Phase transitions of first order and especially phase separations therefore cannot be described by a (homogeneous) canonical ensemble. Taking this serious, fascinating perspectives open for statistical nuclear fragmentation as test ground for the basic principles of statistical mechanics, especially of phase transitions, without the use of the thermodynamic limit. Moreover, there is also a lot of similarity between the accessible phase space of fragmenting nuclei and inhomogeneous multistellar systems. This underlines the fundamental significance for statistical physics in general. (orig.)

Collisionless damping of dust-acoustic waves in a charge varying dusty plasma with nonextensive ions

Energy Technology Data Exchange (ETDEWEB)

Amour, Rabia; Tribeche, Mouloud [Faculty of Physics, Theoretical Physics Laboratory (TPL), Plasma Physics Group (PPG), University of Bab-Ezzouar, USTHB, B.P. 32, El Alia, Algiers 16111 (Algeria)

2014-12-15

The charge variation induced nonlinear dust-acoustic wave damping in a charge varying dusty plasma with nonextensive ions is considered. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust acoustic wave propagation to be described by a damped Korteweg-de Vries (dK-dV) equation the coefficients of which depend sensitively on the nonextensive parameter q. The damping term, solely due to the dust charge variation, is affected by the ion nonextensivity. For the sake of completeness, the possible effects of nonextensivity and collisionless damping on weakly nonlinear wave packets described by the dK-dV equation are succinctly outlined by deriving a nonlinear Schrödinger-like equation with a complex nonlinear coefficient.

Collisionless damping of dust-acoustic waves in a charge varying dusty plasma with nonextensive ions

International Nuclear Information System (INIS)

Amour, Rabia; Tribeche, Mouloud

2014-01-01

The charge variation induced nonlinear dust-acoustic wave damping in a charge varying dusty plasma with nonextensive ions is considered. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust acoustic wave propagation to be described by a damped Korteweg-de Vries (dK-dV) equation the coefficients of which depend sensitively on the nonextensive parameter q. The damping term, solely due to the dust charge variation, is affected by the ion nonextensivity. For the sake of completeness, the possible effects of nonextensivity and collisionless damping on weakly nonlinear wave packets described by the dK-dV equation are succinctly outlined by deriving a nonlinear Schrödinger-like equation with a complex nonlinear coefficient

Predicting fracture of mortar beams under three-point bending using non-extensive statistical modeling of electric emissions

Science.gov (United States)

Stergiopoulos, Ch.; Stavrakas, I.; Triantis, D.; Vallianatos, F.; Stonham, J.

2015-02-01

Weak electric signals termed as 'Pressure Stimulated Currents, PSC' are generated and detected while cement based materials are found under mechanical load, related to the creation of cracks and the consequent evolution of cracks' network in the bulk of the specimen. During the experiment a set of cement mortar beams of rectangular cross-section were subjected to Three-Point Bending (3PB). For each one of the specimens an abrupt mechanical load step was applied, increased from the low load level (Lo) to a high final value (Lh) , where Lh was different for each specimen and it was maintained constant for long time. The temporal behavior of the recorded PSC show that during the load increase a spike-like PSC emission was recorded and consequently a relaxation of the PSC, after reaching its final value, follows. The relaxation process of the PSC was studied using non-extensive statistical physics (NESP) based on Tsallis entropy equation. The behavior of the Tsallis q parameter was studied in relaxation PSCs in order to investigate its potential use as an index for monitoring the crack evolution process with a potential use in non-destructive laboratory testing of cement-based specimens of unknown internal damage level. The dependence of the q-parameter on the Lh (when Lh <0.8Lf), where Lf represents the 3PB strength of the specimen, shows an increase on the q value when the specimens are subjected to gradually higher bending loadings and reaches a maximum value close to 1.4 when the applied Lh becomes higher than 0.8Lf. While the applied Lh becomes higher than 0.9Lf the value of the q-parameter gradually decreases. This analysis of the experimental data manifests that the value of the entropic index q obtains a characteristic decrease while reaching the ultimate strength of the specimen, and thus could be used as a forerunner of the expected failure.

Statistical similarities of pre-earthquake electromagnetic emissions to biological and economic extreme events

Science.gov (United States)

Potirakis, Stelios M.; Contoyiannis, Yiannis; Kopanas, John; Kalimeris, Anastasios; Antonopoulos, George; Peratzakis, Athanasios; Eftaxias, Konstantinos; Nomicos, Costantinos

2014-05-01

When one considers a phenomenon that is "complex" refers to a system whose phenomenological laws that describe the global behavior of the system, are not necessarily directly related to the "microscopic" laws that regulate the evolution of its elementary parts. The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe disparate problems ranging from particle physics to economies of societies. Several authors have suggested that earthquake (EQ) dynamics can be analyzed within similar mathematical frameworks with economy dynamics, and neurodynamics. A central property of the EQ preparation process is the occurrence of coherent large-scale collective behavior with a very rich structure, resulting from repeated nonlinear interactions among the constituents of the system. As a result, nonextensive statistics is an appropriate, physically meaningful, tool for the study of EQ dynamics. Since the fracture induced electromagnetic (EM) precursors are observable manifestations of the underlying EQ preparation process, the analysis of a fracture induced EM precursor observed prior to the occurrence of a large EQ can also be conducted within the nonextensive statistics framework. Within the frame of the investigation for universal principles that may hold for different dynamical systems that are related to the genesis of extreme events, we present here statistical similarities of the pre-earthquake EM emissions related to an EQ, with the pre-ictal electrical brain activity related to an epileptic seizure, and with the pre-crisis economic observables related to the collapse of a share. It is demonstrated the all three dynamical systems' observables can be analyzed in the frame of nonextensive statistical mechanics, while the frequency-size relations of appropriately defined "events" that precede the extreme event related to each one of these different systems present striking quantitative

Generalized statistics and the formation of a quark-gluon plasma

International Nuclear Information System (INIS)

Teweldeberhan, A.M.; Miller, H.G.; Tegen, R.

2003-01-01

The aim of this paper is to investigate the effect of a non-extensive form of statistical mechanics proposed by Tsallis on the formation of a quark-gluon plasma (QGP). We suggest to account for the effects of the dominant part of the long-range interactions among the constituents in the QGP by a change in the statistics of the system in this phase, and we study the relevance of this statistics for the phase transition. The results show that small deviations (≈ 10%) from Boltzmann–Gibbs statistics in the QGP produce a noticeable change in the phase diagram, which can, in principle, be tested experimentally. (author)

Ion-acoustic Gardner solitons in a four-component nonextensive multi-ion plasma

Energy Technology Data Exchange (ETDEWEB)

Jannat, N., E-mail: nilimajannat74@gmail.com; Ferdousi, M.; Mamun, A. A. [Jahangirnagar University, Department of Physics (Bangladesh)

2016-07-15

The nonlinear propagation of ion-acoustic (IA) solitary waves (SWs) in a four-component non-extensive multi-ion plasma system containing inertial positively charged light ions, negatively charged heavy ions, as well as noninertial nonextensive electrons and positrons has been theoretically investigated. The reductive perturbation method has been employed to derive the nonlinear equations, namely, Korteweg−deVries (KdV), modified KdV (mKdV), and Gardner equations. The basic features (viz. polarity, amplitude, width, etc.) of Gardner solitons are found to exist beyond the KdV limit and these IA Gardner solitons are qualitatively different from the KdV and mKdV solitons. It is observed that the basic features of IA SWs are modified by various plasma parameters (viz. electron and positron nonextensivity, electron number density to ion number density, and electron temperature to positron temperature, etc.) of the considered plasma system. The results obtained from this theoretical investigation may be useful in understanding the basic features of IA SWs propagating in both space and laboratory plasmas.

Ion-acoustic Gardner solitons in a four-component nonextensive multi-ion plasma

International Nuclear Information System (INIS)

Jannat, N.; Ferdousi, M.; Mamun, A. A.

2016-01-01

The nonlinear propagation of ion-acoustic (IA) solitary waves (SWs) in a four-component non-extensive multi-ion plasma system containing inertial positively charged light ions, negatively charged heavy ions, as well as noninertial nonextensive electrons and positrons has been theoretically investigated. The reductive perturbation method has been employed to derive the nonlinear equations, namely, Korteweg−deVries (KdV), modified KdV (mKdV), and Gardner equations. The basic features (viz. polarity, amplitude, width, etc.) of Gardner solitons are found to exist beyond the KdV limit and these IA Gardner solitons are qualitatively different from the KdV and mKdV solitons. It is observed that the basic features of IA SWs are modified by various plasma parameters (viz. electron and positron nonextensivity, electron number density to ion number density, and electron temperature to positron temperature, etc.) of the considered plasma system. The results obtained from this theoretical investigation may be useful in understanding the basic features of IA SWs propagating in both space and laboratory plasmas.

Nonextensive Entropy, Prior PDFs and Spontaneous Symmetry Breaking

OpenAIRE

Shafee, Fariel

2008-01-01

We show that using nonextensive entropy can lead to spontaneous symmetry breaking when a parameter changes its value from that applicable for a symmetric domain, as in field theory. We give the physical reasons and also show that even for symmetric Dirichlet priors, such a defnition of the entropy and the parameter value can lead to asymmetry when entropy is maximized.

Generalising the logistic map through the q-product

International Nuclear Information System (INIS)

Pessoa, R W S; Borges, E P

2011-01-01

We investigate a generalisation of the logistic map as x n+1 = 1 - ax n x qmap x n (-1 ≤ x n ≤ 1, 0 map → ∞. The generalisation of this (and others) algebraic operator has been widely used within nonextensive statistical mechanics context (see C. Tsallis, Introduction to Nonextensive Statistical Mechanics, Springer, NY, 2009). We focus the analysis for q map > 1 at the edge of chaos, particularly at the first critical point a c , that depends on the value of q map . Bifurcation diagrams, sensitivity to initial conditions, fractal dimension and rate of entropy growth are evaluated at a c (q map ), and connections with nonextensive statistical mechanics are explored.

Wave Mechanics or Wave Statistical Mechanics

International Nuclear Information System (INIS)

Qian Shangwu; Xu Laizi

2007-01-01

By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.

Higher order nonlinear equations for the dust-acoustic waves in a dusty plasma with two temperature-ions and nonextensive electrons

International Nuclear Information System (INIS)

Emamuddin, M.; Yasmin, S.; Mamun, A. A.

2013-01-01

The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for q c (q>q c ) (where q c is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.

Generalising the logistic map through the q-product

Science.gov (United States)

Pessoa, R. W. S.; Borges, E. P.

2011-03-01

We investigate a generalisation of the logistic map as xn+1 = 1 - axn otimesqmap xn (-1 Borges, E.P. Physica A 340, 95 (2004)]. The usual product, and consequently the usual logistic map, is recovered in the limit q → 1, The tent map is also a particular case for qmap → ∞. The generalisation of this (and others) algebraic operator has been widely used within nonextensive statistical mechanics context (see C. Tsallis, Introduction to Nonextensive Statistical Mechanics, Springer, NY, 2009). We focus the analysis for qmap > 1 at the edge of chaos, particularly at the first critical point ac, that depends on the value of qmap. Bifurcation diagrams, sensitivity to initial conditions, fractal dimension and rate of entropy growth are evaluated at ac(qmap), and connections with nonextensive statistical mechanics are explored.

Self-affinity and nonextensivity of sunspots

International Nuclear Information System (INIS)

Moret, M.A.

2014-01-01

In this paper we study the time series of sunspots by using two different approaches, analyzing its self-affine behavior and studying its distribution. The long-range correlation exponent α has been calculated via Detrended Fluctuation Analysis and the power law vanishes to values greater than 11 years. On the other hand, the distribution of the sunspots obeys a q-exponential decay that suggests a non-extensive behavior. This observed characteristic seems to take an alternative interpretation of the sunspots dynamics. The present findings suggest us to propose a dynamic model of sunspots formation based on a nonlinear Fokker–Planck equation. Therefore its dynamic process follows the generalized thermostatistical formalism.

Behavior of collisional sheath in electronegative plasma with q-nonextensive electron distribution

Science.gov (United States)

Borgohain, Dima Rani; Saharia, K.

2018-03-01

Electronegative plasma sheath is addressed in a collisional unmagnetized plasma consisting of q-nonextensive electrons, Boltzmann distributed negative ions and cold fluid positive ions. Considering the positive ion-neutral collisions and ignoring the effects of ionization and collisions between negative species and positive ions (neutrals), a modified Bohm sheath criterion and hence floating potential are derived by using multifluid model. Using the modified Bohm sheath criterion, the sheath characteristics such as spatial profiles of density, potential and net space charge density have been numerically investigated. It is found that increasing values of q-nonextensivity, electronegativity and collisionality lead to a decrease of the sheath thickness and an increase of the sheath potential and the net space charge density. With increasing values of the electron temperature to negative ion temperature ratio, the sheath thickness increases and the sheath potential as well as the net space charge density in the sheath region decreases.

Equilibrium statistical mechanics

CERN Document Server

Jackson, E Atlee

2000-01-01

Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t

Equilibrium statistical mechanics

CERN Document Server

Mayer, J E

1968-01-01

The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight t

Landau damping of dust acoustic waves in the presence of hybrid nonthermal nonextensive electrons

Science.gov (United States)

El-Taibany, W. F.; Zedan, N. A.; Taha, R. M.

2018-06-01

Based on the kinetic theory, Landau damping of dust acoustic waves (DAWs) propagating in a dusty plasma composed of hybrid nonthermal nonextensive distributed electrons, Maxwellian distributed ions and negatively charged dust grains is investigated using Vlasov-Poisson's equations. The characteristics of the DAWs Landau damping are discussed. It is found that the wave frequency increases by decreasing (increasing) the value of nonextensive (nonthermal) parameter, q (α ). It is recognized that α plays a significant role in observing damping or growing DAW oscillations. For small values of α , damping modes have been observed until reaching a certain value of α at which ω i vanishes, then a growing mode appears in the case of superextensive electrons. However, only damping DAW modes are observed in case of subextensive electrons. The present study is useful in the space situations where such distribution exists.

Effects of nonextensivity on the electron-acoustic solitary structures in a magnetized electron−positron−ion plasma

Energy Technology Data Exchange (ETDEWEB)

Rafat, A., E-mail: rafat.plasma@gmail.com; Rahman, M. M.; Alam, M. S.; Mamun, A. A. [Jahangirnagar University, Department of Physics (Bangladesh)

2016-08-15

Obliquely propagating electron-acoustic solitary waves (EASWs) in a magnetized electron−positron−ion plasma (containing nonextensive hot electrons and positrons, inertial cold electrons, and immobile positive ions) are precisely investigated by deriving the Zakharov–Kuznetsov equation. It is found that the basic features (viz. polarity, amplitude, width, phase speed, etc.) of the EASWs are significantly modified by the effects of the external magnetic field, obliqueness of the system, nonextensivity of hot positrons and electrons, ratio of the hot electron temperature to the hot positron temperature, and ratio of the cold electron number density to the hot positron number density. The findings of our results can be employed in understanding the localized electrostatic structures and the characteristics of EASWs in various astrophysical plasmas.

Study of quantum hadronic states using new optimum principles and new coherent production mechanisms

International Nuclear Information System (INIS)

Ion, D. B.; Ion, M. L.; Ion-Mihai, R.

2002-01-01

We introduced a new kind of quantum entropy for quantum scattering: conjugated nonextensivity entropy S Jθ bar (p,q). Using this new kind of nonextensive entropy we studied the nonextensive quantum scattering states of the hadronic interactions. We proved that probability distributions produced at quantum equilibrium coincide with optimal distributions given by the principle of minimum distance in the space of quantum scattering states. Using optimal states we proved new uncertainty relations and new entropic bands: For experimental tests we used the available phase shifts for the pion-nucleus scatterings and also for the pion-nucleon scatterings. Experimental tests of entropic bands and principle of maximum entropy for conjugated nonextensivity entropy are compared with entropic bands for usual entropy of joint probability S Jθ bar (p) and for pion-nucleus scatterings. Also given are the experimental tests of entropic bands and principle of maximum entropy for conjugated nonextensivity entropy compared with entropic bands for usual entropy of joint probability S Jθ bar (p) and for pion-nucleon scatterings.Our experimental tests proved the existence of the principle of limited entropic uncertainty in hadronic scattering. The experimental tests showed clearly that quantum elastic scattering is well described by the principle of minimum distance in the space of quantum states. By these results we obtained strong evidence for the nonextensivity of the hadronic scattering statistics. (authors)

Statistical mechanics

CERN Document Server

Davidson, Norman

2003-01-01

Clear and readable, this fine text assists students in achieving a grasp of the techniques and limitations of statistical mechanics. The treatment follows a logical progression from elementary to advanced theories, with careful attention to detail and mathematical development, and is sufficiently rigorous for introductory or intermediate graduate courses.Beginning with a study of the statistical mechanics of ideal gases and other systems of non-interacting particles, the text develops the theory in detail and applies it to the study of chemical equilibrium and the calculation of the thermody

A no extensive statistical model for the nucleon structure function

International Nuclear Information System (INIS)

Trevisan, Luis A.; Mirez, Carlos

2013-01-01

We studied an application of nonextensive thermodynamics to describe the structure function of nucleon, in a model where the usual Fermi-Dirac and Bose-Einstein energy distribution were replaced by the equivalent functions of the q-statistical. The parameters of the model are given by an effective temperature T, the q parameter (from Tsallis statistics), and two chemical potentials given by the corresponding up (u) and down (d) quark normalization in the nucleon.

Nonextensive kinetic theory and H-theorem in general relativity

Science.gov (United States)

Santos, A. P.; Silva, R.; Alcaniz, J. S.; Lima, J. A. S.

2017-11-01

The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is shown that Tsallis entropic framework satisfies a H-theorem in the presence of gravitational fields. Consistency with the 2nd law of thermodynamics is obtained only whether the entropic q-parameter lies in the interval q ∈ [ 0 , 2 ] . As occurs in the absence of gravitational fields, it is also proved that the local collisional equilibrium is described by the extended Bose-Einstein (Fermi-Dirac) q-distributions.

Lectures on statistical mechanics

CERN Document Server

Bowler, M G

1982-01-01

Anyone dissatisfied with the almost ritual dullness of many 'standard' texts in statistical mechanics will be grateful for the lucid explanation and generally reassuring tone. Aimed at securing firm foundations for equilibrium statistical mechanics, topics of great subtlety are presented transparently and enthusiastically. Very little mathematical preparation is required beyond elementary calculus and prerequisites in physics are limited to some elementary classical thermodynamics. Suitable as a basis for a first course in statistical mechanics, the book is an ideal supplement to more convent

Statistical mechanics

CERN Document Server

Schwabl, Franz

2006-01-01

The completely revised new edition of the classical book on Statistical Mechanics covers the basic concepts of equilibrium and non-equilibrium statistical physics. In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis - the form of the microcanonical density matrix - this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications to critical dynamics, kinetic theories, as well as fundamental considerations of irreversibility, are discussed. The text will be useful for advanced students of physics and other natural sciences; a basic knowledge of quantum mechan...

Statistical mechanics

CERN Document Server

Jana, Madhusudan

2015-01-01

Statistical mechanics is self sufficient, written in a lucid manner, keeping in mind the exam system of the universities. Need of study this subject and its relation to Thermodynamics is discussed in detail. Starting from Liouville theorem gradually, the Statistical Mechanics is developed thoroughly. All three types of Statistical distribution functions are derived separately with their periphery of applications and limitations. Non-interacting ideal Bose gas and Fermi gas are discussed thoroughly. Properties of Liquid He-II and the corresponding models have been depicted. White dwarfs and condensed matter physics, transport phenomenon - thermal and electrical conductivity, Hall effect, Magneto resistance, viscosity, diffusion, etc. are discussed. Basic understanding of Ising model is given to explain the phase transition. The book ends with a detailed coverage to the method of ensembles (namely Microcanonical, canonical and grand canonical) and their applications. Various numerical and conceptual problems ar...

Statistical mechanics of nonequilibrium liquids

CERN Document Server

Evans, Denis J; Craig, D P; McWeeny, R

1990-01-01

Statistical Mechanics of Nonequilibrium Liquids deals with theoretical rheology. The book discusses nonlinear response of systems and outlines the statistical mechanical theory. In discussing the framework of nonequilibrium statistical mechanics, the book explains the derivation of a nonequilibrium analogue of the Gibbsian basis for equilibrium statistical mechanics. The book reviews the linear irreversible thermodynamics, the Liouville equation, and the Irving-Kirkwood procedure. The text then explains the Green-Kubo relations used in linear transport coefficients, the linear response theory,

Nonextensive thermodynamics with finite chemical potentials and protoneutron starss⋆,⋆⋆

Directory of Open Access Journals (Sweden)

Megías Eugenio

2014-01-01

Full Text Available We derive the nonextensive thermodynamics of an ideal quantum gas composed by bosons and/or fermions with finite chemical potentials. We find agreement with previous works when μ ≤ m, and some inconsistencies are corrected for fermions when μ > m. This formalism is then used to study the thermodynamical properties of hadronic systems based on a Hadron Resonance Gas approach. We apply this result to study the protoneutron star stability under several conditions.

Planar and nonplanar electron-acoustic solitary waves in a plasma with a q-nonextensive electron velocity distribution

International Nuclear Information System (INIS)

Han, Jiu-Ning; Luo, Jun-Hua; Sun, Gui-Hua; Liu, Zhen-Lai; Ge, Su-Hong; Wang, Xin-Xing; Li, Jun-Xiu

2014-01-01

The nonlinear dynamics of nonplanar (cylindrical and spherical) electron-acoustic solitary wave structures in an unmagnetized, collisionless plasma composed of stationary ions, cold fluid electrons and hot q-nonextensive distributed electrons are theoretically studied. We discuss the effects of the nonplanar geometry, nonextensivity of hot electrons and ‘hot’ to ‘cold’ electron number density ratio on the time evolution characters of cylindrical and spherical solitary waves. Moreover, the effects of plasma parameters on the nonlinear structure induced by the interaction between two planar solitary waves are also investigated. It is found that these plasma parameters have significant influences on the properties of the above-mentioned nonlinear structures. Our theoretical study may be useful to understand the nonlinear features of electron-acoustic wave structures in astrophysical plasma systems. (paper)

Statistical mechanics of superconductivity

CERN Document Server

Kita, Takafumi

2015-01-01

This book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch–De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction, and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree–Fock equations, and Landau’s Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematical clarity based on ...

Statistical mechanics in JINR

International Nuclear Information System (INIS)

Tonchev, N.; Shumovskij, A.S.

1986-01-01

The history of investigations, conducted at the JINR in the field of statistical mechanics, beginning with the fundamental works by Bogolyubov N.N. on superconductivity microscopic theory is presented. Ideas, introduced in these works and methods developed in them, have largely determined the ways for developing statistical mechanics in the JINR and Hartree-Fock-Bogolyubov variational principle has become an important method of the modern nucleus theory. A brief review of the main achievements, connected with the development of statistical mechanics methods and their application in different fields of physical science is given

Effects of dust polarity and nonextensive electrons on the dust-ion acoustic solitons and double layers in earth atmosphere

Science.gov (United States)

Ghobakhloo, Marzieh; Zomorrodian, Mohammad Ebrahim; Javidan, Kurosh

2018-05-01

Propagation of dustion acoustic solitary waves (DIASWs) and double layers is discussed in earth atmosphere, using the Sagdeev potential method. The best model for distribution function of electrons in earth atmosphere is found by fitting available data on different distribution functions. The nonextensive function with parameter q = 0.58 provides the best fit on observations. Thus we analyze the propagation of localized waves in an unmagnetized plasma containing nonextensive electrons, inertial ions, and negatively/positively charged stationary dust. It is found that both compressive and rarefactive solitons as well as double layers exist depending on the sign (and the value) of dust polarity. Characters of propagated waves are described using the presented model.

How different are ICT-supported pedagogical practices from extensive and non-extensive ICT-using science teachers?

NARCIS (Netherlands)

Voogt, Joke

2009-01-01

This paper aims to understand the differences between characteristics of ICT-supported pedagogical practices of grade 8 science teachers of extensive and non-extensive ICT-using science teachers. The differences of the pedagogical practices are described in terms of innovative and traditionally

Nonextensive entropy interdisciplinary applications

CERN Document Server

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.

Nonlinear ion-acoustic structures in a nonextensive electron–positron–ion–dust plasma: Modulational instability and rogue waves

Energy Technology Data Exchange (ETDEWEB)

Guo, Shimin, E-mail: gsm861@126.com [School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 (China); Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG (Netherlands); Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn [School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 (China); Center for Computational Geosciences, Xi’an Jiaotong University, Xi’an, 710049 (China); Sun, Anbang [Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG (Netherlands)

2013-05-15

The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time.

Nonlinear ion-acoustic structures in a nonextensive electron–positron–ion–dust plasma: Modulational instability and rogue waves

International Nuclear Information System (INIS)

Guo, Shimin; Mei, Liquan; Sun, Anbang

2013-01-01

The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time

Statistical mechanics in a nutshell

CERN Document Server

Peliti, Luca

2011-01-01

Statistical mechanics is one of the most exciting areas of physics today, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. Statistical Mechanics in a Nutshell offers the most concise, self-contained introduction to this rapidly developing field. Requiring only a background in elementary calculus and elementary mechanics, this book starts with the basics, introduces the most important developments in classical statistical mechanics over the last thirty years, and guides readers to the very threshold of today

Einstein's statistical mechanics

Energy Technology Data Exchange (ETDEWEB)

Baracca, A; Rechtman S, R

1985-08-01

The foundation of equilibrium classical statistical mechanics were laid down in 1902 independently by Gibbs and Einstein. The latter's contribution, developed in three papers published between 1902 and 1904, is usually forgotten and when not, rapidly dismissed as equivalent to Gibb's. We review in detail Einstein's ideas on the foundations of statistical mechanics and show that they constitute the beginning of a research program that led Einstein to quantum theory. We also show how these ideas may be used as a starting point for an introductory course on the subject.

Einstein's statistical mechanics

International Nuclear Information System (INIS)

Baracca, A.; Rechtman S, R.

1985-01-01

The foundation of equilibrium classical statistical mechanics were laid down in 1902 independently by Gibbs and Einstein. The latter's contribution, developed in three papers published between 1902 and 1904, is usually forgotten and when not, rapidly dismissed as equivalent to Gibb's. We review in detail Einstein's ideas on the foundations of statistical mechanics and show that they constitute the beginning of a research program that led Einstein to quantum theory. We also show how these ideas may be used as a starting point for an introductory course on the subject. (author)

On the Impact of Tsallis Statistics on Cosmic Ray Showers

Directory of Open Access Journals (Sweden)

M. Abrahão

2016-01-01

Full Text Available We investigate the impact of the Tsallis nonextensive statistics introduced by intrinsic temperature fluctuations in p-Air ultrahigh energy interactions on observables of cosmic ray showers, such as the slant depth of the maximum Xmax and the muon number on the ground Nμ. The results show that these observables are significantly affected by temperature fluctuations and agree qualitatively with the predictions of Heitler model.

(3 + 1)-dimensional cylindrical Korteweg-de Vries equation for nonextensive dust acoustic waves: Symbolic computation and exact solutions

International Nuclear Information System (INIS)

Guo Shimin; Wang Hongli; Mei Liquan

2012-01-01

By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.

Quantum mechanics from classical statistics

International Nuclear Information System (INIS)

Wetterich, C.

2010-01-01

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

Statistical mechanics rigorous results

CERN Document Server

Ruelle, David

1999-01-01

This classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work. The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century.

The q-Statistics and QCD Thermodynamics at LHC

CERN Document Server

Bhattacharyya, Trambak; Sahoo, Pragati; Garg, Prakhar; Pareek, Pooja; Sahoo, Raghunath; Cleymans, Jean

2016-01-01

We perform a Taylor series expansion of Tsallis distribution by assuming the Tsallis parameter $q$ close to 1. The $q$ value shows the deviation of a system from a thermalised Boltzmann distribution. By taking up to first order in $(q-1)$, we derive an analytical result for Tsallis distribution including radial flow. Further, in the present work, we also study the speed of sound ($c_s$) as a function of temperature using the non-extensive Tsallis statistics for different $q$ values and for different mass cut-offs.

A statistical mechanical interpretation of algorithmic information theory: Total statistical mechanical interpretation based on physical argument

International Nuclear Information System (INIS)

Tadaki, Kohtaro

2010-01-01

The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp. 425-434, 2008] and [K. Tadaki, Proceedings of LFCS'09, Springer's LNCS, vol. 5407, pp. 422-440, 2009], where we introduced the notion of thermodynamic quantities, such as partition function Z(T), free energy F(T), energy E(T), statistical mechanical entropy S(T), and specific heat C(T), into AIT. We then discovered that, in the interpretation, the temperature T equals to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate by means of program-size complexity. Furthermore, we showed that this situation holds for the temperature T itself, which is one of the most typical thermodynamic quantities. Namely, we showed that, for each of the thermodynamic quantities Z(T), F(T), E(T), and S(T) above, the computability of its value at temperature T gives a sufficient condition for T is an element of (0,1) to satisfy the condition that the partial randomness of T equals to T. In this paper, based on a physical argument on the same level of mathematical strictness as normal statistical mechanics in physics, we develop a total statistical mechanical interpretation of AIT which actualizes a perfect correspondence to normal statistical mechanics. We do this by identifying a microcanonical ensemble in the framework of AIT. As a result, we clarify the statistical mechanical meaning of the thermodynamic quantities of AIT.

A Tsallis’ statistics based neural network model for novel word learning

Science.gov (United States)

Hadzibeganovic, Tarik; Cannas, Sergio A.

2009-03-01

We invoke the Tsallis entropy formalism, a nonextensive entropy measure, to include some degree of non-locality in a neural network that is used for simulation of novel word learning in adults. A generalization of the gradient descent dynamics, realized via nonextensive cost functions, is used as a learning rule in a simple perceptron. The model is first investigated for general properties, and then tested against the empirical data, gathered from simple memorization experiments involving two populations of linguistically different subjects. Numerical solutions of the model equations corresponded to the measured performance states of human learners. In particular, we found that the memorization tasks were executed with rather small but population-specific amounts of nonextensivity, quantified by the entropic index q. Our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems.

Quantum mechanics as applied mathematical statistics

International Nuclear Information System (INIS)

Skala, L.; Cizek, J.; Kapsa, V.

2011-01-01

Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

Statistical mechanics principles and selected applications

CERN Document Server

Hill, Terrell L

1956-01-01

""Excellent … a welcome addition to the literature on the subject."" - ScienceBefore the publication of this standard, oft-cited book, there were few if any statistical-mechanics texts that incorporated reviews of both fundamental principles and recent developments in the field.In this volume, Professor Hill offers just such a dual presentation - a useful account of basic theory and of its applications, made accessible in a comprehensive format. The book opens with concise, unusually clear introductory chapters on classical statistical mechanics, quantum statistical mechanics and the relatio

BIG BANG NUCLEOSYNTHESIS WITH A NON-MAXWELLIAN DISTRIBUTION

International Nuclear Information System (INIS)

Bertulani, C. A.; Fuqua, J.; Hussein, M. S.

2013-01-01

The abundances of light elements based on the big bang nucleosynthesis model are calculated using the Tsallis non-extensive statistics. The impact of the variation of the non-extensive parameter q from the unity value is compared to observations and to the abundance yields from the standard big bang model. We find large differences between the reaction rates and the abundance of light elements calculated with the extensive and the non-extensive statistics. We found that the observations are consistent with a non-extensive parameter q = 1 - 0.12 +0.05 , indicating that a large deviation from the Boltzmann-Gibbs statistics (q = 1) is highly unlikely.

How different are ICT-supported pedagogical practices from extensive and non-extensive ICT-using science teachers?

OpenAIRE

Voogt, Joke

2009-01-01

This paper aims to understand the differences between characteristics of ICT-supported pedagogical practices of grade 8 science teachers of extensive and non-extensive ICT-using science teachers. The differences of the pedagogical practices are described in terms of innovative and traditionally important practice orientations. The innovative practice orientation reflects a demand for education in an information society (e.g. communication skills; ability to learn at own pace), while the tradi...

The scientifiv way of thinking in statistics, statistical physics and quantum mechanics

OpenAIRE

Săvoiu, Gheorghe

2008-01-01

This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...

The scientific way of thinking in statistics, statistical physics and quantum mechanics

OpenAIRE

Săvoiu, Gheorghe

2008-01-01

This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...

Statistical mechanics of anyons

International Nuclear Information System (INIS)

Arovas, D.P.

1985-01-01

We study the statistical mechanics of a two-dimensional gas of free anyons - particles which interpolate between Bose-Einstein and Fermi-Dirac character. Thermodynamic quantities are discussed in the low-density regime. In particular, the second virial coefficient is evaluated by two different methods and is found to exhibit a simple, periodic, but nonanalytic behavior as a function of the statistics determining parameter. (orig.)

Multiplicity dependence of non-extensive parameters for strange and multi-strange particles in proton-proton collisions at √(s) = 7 TeV at the LHC

Energy Technology Data Exchange (ETDEWEB)

Khuntia, Arvind; Tripathy, Sushanta; Sahoo, Raghunath [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Sciences, Indore (India); Cleymans, Jean [University of Cape Town, UCT-CERN Research Centre and Department of Physics, Rondebosch (South Africa)

2017-05-15

The transverse momentum (p{sub T}) spectra in proton-proton collisions at √(s) = 7 TeV, measured by the ALICE experiment at the LHC are analyzed with a thermodynamically consistent Tsallis distribution. The information about the freeze-out surface in terms of freeze-out volume, temperature and the non-extensivity parameter, q, for K{sup 0}{sub S}, Λ + anti Λ, Ξ{sup -} + anti Ξ{sup +} and Ω{sup -} + anti Ω{sup +} are extracted by fitting the p{sub T} spectra with the Tsallis distribution function. The freeze-out parameters of these particles are studied as a function of the charged particle multiplicity density (dN{sub ch}/dη). In addition, we also study these parameters as a function of the particle mass to see any possible mass ordering. The strange and multi-strange particles show mass ordering in volume, temperature, non-extensive parameter and also a strong dependence on multiplicity classes. It is observed that with increase in particle multiplicity, the non-extensivity parameter, q decreases, which indicates the tendency of the produced system towards thermodynamic equilibration. The increase in strange particle multiplicity is observed to be due to the increase of temperature and may not be due to the size of the freeze-out volume. (orig.)

Multiplicity dependence of non-extensive parameters for strange and multi-strange particles in proton-proton collisions at √(s) = 7 TeV at the LHC

International Nuclear Information System (INIS)

Khuntia, Arvind; Tripathy, Sushanta; Sahoo, Raghunath; Cleymans, Jean

2017-01-01

The transverse momentum (p T ) spectra in proton-proton collisions at √(s) = 7 TeV, measured by the ALICE experiment at the LHC are analyzed with a thermodynamically consistent Tsallis distribution. The information about the freeze-out surface in terms of freeze-out volume, temperature and the non-extensivity parameter, q, for K 0 S , Λ + anti Λ, Ξ - + anti Ξ + and Ω - + anti Ω + are extracted by fitting the p T spectra with the Tsallis distribution function. The freeze-out parameters of these particles are studied as a function of the charged particle multiplicity density (dN ch /dη). In addition, we also study these parameters as a function of the particle mass to see any possible mass ordering. The strange and multi-strange particles show mass ordering in volume, temperature, non-extensive parameter and also a strong dependence on multiplicity classes. It is observed that with increase in particle multiplicity, the non-extensivity parameter, q decreases, which indicates the tendency of the produced system towards thermodynamic equilibration. The increase in strange particle multiplicity is observed to be due to the increase of temperature and may not be due to the size of the freeze-out volume. (orig.)

Modern Thermodynamics with Statistical Mechanics

CERN Document Server

Helrich, Carl S

2009-01-01

With the aim of presenting thermodynamics in as simple and as unified a form as possible, this textbook starts with an introduction to the first and second laws and then promptly addresses the complete set of the potentials in a subsequent chapter and as a central theme throughout. Before discussing modern laboratory measurements, the book shows that the fundamental quantities sought in the laboratory are those which are required for determining the potentials. Since the subjects of thermodynamics and statistical mechanics are a seamless whole, statistical mechanics is treated as integral part of the text. Other key topics such as irreversibility, the ideas of Ilya Prigogine, chemical reaction rates, equilibrium of heterogeneous systems, and transition-state theory serve to round out this modern treatment. An additional chapter covers quantum statistical mechanics due to active current research in Bose-Einstein condensation. End-of-chapter exercises, chapter summaries, and an appendix reviewing fundamental pr...

Playing at Statistical Mechanics

Science.gov (United States)

Clark, Paul M.; And Others

1974-01-01

Discussed are the applications of counting techniques of a sorting game to distributions and concepts in statistical mechanics. Included are the following distributions: Fermi-Dirac, Bose-Einstein, and most probable. (RH)

Semiclassical statistical mechanics

International Nuclear Information System (INIS)

Stratt, R.M.

1979-04-01

On the basis of an approach devised by Miller, a formalism is developed which allows the nonperturbative incorporation of quantum effects into equilibrium classical statistical mechanics. The resulting expressions bear a close similarity to classical phase space integrals and, therefore, are easily molded into forms suitable for examining a wide variety of problems. As a demonstration of this, three such problems are briefly considered: the simple harmonic oscillator, the vibrational state distribution of HCl, and the density-independent radial distribution function of He 4 . A more detailed study is then made of two more general applications involving the statistical mechanics of nonanalytic potentials and of fluids. The former, which is a particularly difficult problem for perturbative schemes, is treated with only limited success by restricting phase space and by adding an effective potential. The problem of fluids, however, is readily found to yield to a semiclassical pairwise interaction approximation, which in turn permits any classical many-body model to be expressed in a convenient form. The remainder of the discussion concentrates on some ramifications of having a phase space version of quantum mechanics. To test the breadth of the formulation, the task of constructing quantal ensemble averages of phase space functions is undertaken, and in the process several limitations of the formalism are revealed. A rather different approach is also pursued. The concept of quantum mechanical ergodicity is examined through the use of numerically evaluated eigenstates of the Barbanis potential, and the existence of this quantal ergodicity - normally associated with classical phase space - is verified. 21 figures, 4 tables

Emergence of quantum mechanics from classical statistics

International Nuclear Information System (INIS)

Wetterich, C

2009-01-01

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables 'measure' properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.

The existence of electron-acoustic shock waves and their interactions in a non-Maxwellian plasma with q-nonextensive distributed electrons

Energy Technology Data Exchange (ETDEWEB)

Han, Jiu-Ning; He, Yong-Lin; Han, Zhen-Hai; Dong, Guang-Xing; Nan, Ya-Gong [College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China); Li, Jun-Xiu [College of Civil Engineering, Hexi University, Zhangye 734000 (China)

2013-07-15

We present a theoretical investigation for the nonlinear interaction between electron-acoustic shock waves in a nonextensive two-electron plasma. The interaction is governed by a pair of Korteweg-de Vries-Burgers equations. We focus on studying the colliding effects on the propagation of shock waves, more specifically, we have studied the effects of plasma parameters, i.e., the nonextensive parameter q, the “hot” to “cold” electron number density ratio α, and the normalized electron kinematic viscosity η{sub 0} on the trajectory changes (phase shifts) of shock waves. It is found that there are trajectory changes (phase shifts) for both colliding shock waves in the present plasma system. We also noted that the nonlinearity has no decisive effect on the trajectory changes, the occurrence of trajectory changes may be due to the combined role played by the dispersion and dissipation of the nonlinear structure. Our theoretical study may be beneficial to understand the propagation and interaction of nonlinear electrostatic waves and may brings a possibility to develop the nonlinear theory of electron-acoustic waves in astrophysical plasma systems.

Analogies between classical statistical mechanics and quantum mechanics

International Nuclear Information System (INIS)

Uehara, M.

1986-01-01

Some analogies between nonequilibrium classical statistical mechanics and quantum mechanics, at the level of the Liouville equation and at the kinetic level, are commented on. A theorem, related to the Vlasov equation applied to a plasma, is proved. The theorem presents an analogy with Ehrenfest's theorem of quantum mechanics. An analogy between the plasma kinetic theory and Bohm's quantum theory with 'hidden variables' is also shown. (Author) [pt

The large deviation approach to statistical mechanics

International Nuclear Information System (INIS)

Touchette, Hugo

2009-01-01

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.

The large deviation approach to statistical mechanics

Science.gov (United States)

Touchette, Hugo

2009-07-01

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein’s theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.

QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

International Nuclear Information System (INIS)

Geiger, G.

2000-01-01

The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory

Statistical-mechanical entropy by the thin-layer method

International Nuclear Information System (INIS)

Feng, He; Kim, Sung Won

2003-01-01

G. Hooft first studied the statistical-mechanical entropy of a scalar field in a Schwarzschild black hole background by the brick-wall method and hinted that the statistical-mechanical entropy is the statistical origin of the Bekenstein-Hawking entropy of the black hole. However, according to our viewpoint, the statistical-mechanical entropy is only a quantum correction to the Bekenstein-Hawking entropy of the black-hole. The brick-wall method based on thermal equilibrium at a large scale cannot be applied to the cases out of equilibrium such as a nonstationary black hole. The statistical-mechanical entropy of a scalar field in a nonstationary black hole background is calculated by the thin-layer method. The condition of local equilibrium near the horizon of the black hole is used as a working postulate and is maintained for a black hole which evaporates slowly enough and whose mass is far greater than the Planck mass. The statistical-mechanical entropy is also proportional to the area of the black hole horizon. The difference from the stationary black hole is that the result relies on a time-dependent cutoff

Graphene Statistical Mechanics

Science.gov (United States)

Bowick, Mark; Kosmrlj, Andrej; Nelson, David; Sknepnek, Rastko

2015-03-01

Graphene provides an ideal system to test the statistical mechanics of thermally fluctuating elastic membranes. The high Young's modulus of graphene means that thermal fluctuations over even small length scales significantly stiffen the renormalized bending rigidity. We study the effect of thermal fluctuations on graphene ribbons of width W and length L, pinned at one end, via coarse-grained Molecular Dynamics simulations and compare with analytic predictions of the scaling of width-averaged root-mean-squared height fluctuations as a function of distance along the ribbon. Scaling collapse as a function of W and L also allows us to extract the scaling exponent eta governing the long-wavelength stiffening of the bending rigidity. A full understanding of the geometry-dependent mechanical properties of graphene, including arrays of cuts, may allow the design of a variety of modular elements with desired mechanical properties starting from pure graphene alone. Supported by NSF grant DMR-1435794

Entropy: A Unifying Path for Understanding Complexity in Natural, Artificial and Social Systems

Science.gov (United States)

2011-07-01

details can be seen. Figure 24 – Rank frequency functions of plays ( Shakespeare ) and books (Dickens) fitted by the generalizations of the...0-387-75888-6]. [4] Tsallis, C. (2009b). Introduction to Nonextensive Statistical Mechanics - Approaching a Complex World. (Springer, New York

Nonequilibrium statistical mechanics ensemble method

CERN Document Server

Eu, Byung Chan

1998-01-01

In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium Audience This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena

Introduction to quantum statistical mechanics

International Nuclear Information System (INIS)

Bogolyubov, N.N.; Bogolyubov, N.N.

1980-01-01

In a set of lectures, which has been delivered at the Physical Department of Moscow State University as a special course for students represented are some basic ideas of quantum statistical mechanics. Considered are in particular, the Liouville equations in classical and quantum mechanics, canonical distribution and thermodynamical functions, two-time correlation functions and Green's functions in the theory of thermal equilibrium

Net-baryon number fluctuations using Tsallis statistics

International Nuclear Information System (INIS)

Garg, P.; Singh, B.K.; Mishra, D.K.; Netrakanti, P.K.; Mohanty, A.K.

2014-01-01

In the present work, we show that the HRG-Tsallis model with a temperature dependent nonextensive q parameter reproduces the energy dependence of Sσ and kσ 2 for most peripheral collisions as well as Sσ for central collisions. However, the energy dependence of kσ 2 of central collision deviate significantly from the HRG-Tsallis model predictions particularly at energies 19.6 GeV and 27 GeV. We argue here that the predictions of HRG-Tsallis characterized by a temperature dependent q parameter should be taken as the baseline to study (experimentally) fluctuations of dynamical origin if any, which is still not contained in the Tsallis non-extensive thermodynamics

An introduction to thermodynamics and statistical mechanics

CERN Document Server

Saxena, A K

2016-01-01

An Introduction to Thermodynamics and Statistical Mechanics aims to serve as a text book for undergraduate hons.and postgraduate students of physics. The book covers First Law of Thermodynamics, Entropy and Second Law ofThermodynamics, Thermodynamic Relations, The Statistical Basis of Thermodynamics, Microcanonical Ensemble,Classical Statistical and Canonical Distribution, Grand Canonical Ensemble, Quantum Statistical Mechanics, PhaseTransitions, Fluctuations, Irreversible Processes and Transport Phenomena (Diffusion).SALIENT FEATURES:iC* Offers students a conceptual development of the subjectiC* Review questions at the end of chapters.NEW TO THE SECOND EDITIONiC* PVT SurfacesiC* Real Heat EnginesiC* Van der Waals Models (Qualitative Considerations)iC* Cluster ExpansioniC* Brownian Motion (Einstein's Theory)

Statistical mechanics of economics I

Energy Technology Data Exchange (ETDEWEB)

Kusmartsev, F.V., E-mail: F.Kusmartsev@lboro.ac.u [Department of Physics, Loughborough University, Leicestershire, LE11 3TU (United Kingdom)

2011-02-07

We show that statistical mechanics is useful in the description of financial crisis and economics. Taking a large amount of instant snapshots of a market over an interval of time we construct their ensembles and study their statistical interference. This results in a probability description of the market and gives capital, money, income, wealth and debt distributions, which in the most cases takes the form of the Bose-Einstein distribution. In addition, statistical mechanics provides the main market equations and laws which govern the correlations between the amount of money, debt, product, prices and number of retailers. We applied the found relations to a study of the evolution of the economics in USA between the years 1996 to 2008 and observe that over that time the income of a major population is well described by the Bose-Einstein distribution which parameters are different for each year. Each financial crisis corresponds to a peak in the absolute activity coefficient. The analysis correctly indicates the past crises and predicts the future one.

Statistical mechanics of economics I

International Nuclear Information System (INIS)

Kusmartsev, F.V.

2011-01-01

We show that statistical mechanics is useful in the description of financial crisis and economics. Taking a large amount of instant snapshots of a market over an interval of time we construct their ensembles and study their statistical interference. This results in a probability description of the market and gives capital, money, income, wealth and debt distributions, which in the most cases takes the form of the Bose-Einstein distribution. In addition, statistical mechanics provides the main market equations and laws which govern the correlations between the amount of money, debt, product, prices and number of retailers. We applied the found relations to a study of the evolution of the economics in USA between the years 1996 to 2008 and observe that over that time the income of a major population is well described by the Bose-Einstein distribution which parameters are different for each year. Each financial crisis corresponds to a peak in the absolute activity coefficient. The analysis correctly indicates the past crises and predicts the future one.

Learning Predictive Statistics: Strategies and Brain Mechanisms.

Science.gov (United States)

Wang, Rui; Shen, Yuan; Tino, Peter; Welchman, Andrew E; Kourtzi, Zoe

2017-08-30

When immersed in a new environment, we are challenged to decipher initially incomprehensible streams of sensory information. However, quite rapidly, the brain finds structure and meaning in these incoming signals, helping us to predict and prepare ourselves for future actions. This skill relies on extracting the statistics of event streams in the environment that contain regularities of variable complexity from simple repetitive patterns to complex probabilistic combinations. Here, we test the brain mechanisms that mediate our ability to adapt to the environment's statistics and predict upcoming events. By combining behavioral training and multisession fMRI in human participants (male and female), we track the corticostriatal mechanisms that mediate learning of temporal sequences as they change in structure complexity. We show that learning of predictive structures relates to individual decision strategy; that is, selecting the most probable outcome in a given context (maximizing) versus matching the exact sequence statistics. These strategies engage distinct human brain regions: maximizing engages dorsolateral prefrontal, cingulate, sensory-motor regions, and basal ganglia (dorsal caudate, putamen), whereas matching engages occipitotemporal regions (including the hippocampus) and basal ganglia (ventral caudate). Our findings provide evidence for distinct corticostriatal mechanisms that facilitate our ability to extract behaviorally relevant statistics to make predictions. SIGNIFICANCE STATEMENT Making predictions about future events relies on interpreting streams of information that may initially appear incomprehensible. Past work has studied how humans identify repetitive patterns and associative pairings. However, the natural environment contains regularities that vary in complexity from simple repetition to complex probabilistic combinations. Here, we combine behavior and multisession fMRI to track the brain mechanisms that mediate our ability to adapt to

Statistical mechanics and applications in condensed matter

CERN Document Server

Di Castro, Carlo

2015-01-01

This innovative and modular textbook combines classical topics in thermodynamics, statistical mechanics and many-body theory with the latest developments in condensed matter physics research. Written by internationally renowned experts and logically structured to cater for undergraduate and postgraduate students and researchers, it covers the underlying theoretical principles and includes numerous problems and worked examples to put this knowledge into practice. Three main streams provide a framework for the book; beginning with thermodynamics and classical statistical mechanics, including mean field approximation, fluctuations and the renormalization group approach to critical phenomena. The authors then examine quantum statistical mechanics, covering key topics such as normal Fermi and Luttinger liquids, superfluidity and superconductivity. Finally, they explore classical and quantum kinetics, Anderson localization and quantum interference, and disordered Fermi liquids. Unique in providing a bridge between ...

Tsallis’ non-extensive free energy as a subjective value of an uncertain reward

Science.gov (United States)

Takahashi, Taiki

2009-03-01

Recent studies in neuroeconomics and econophysics revealed the importance of reward expectation in decision under uncertainty. Behavioral neuroeconomic studies have proposed that the unpredictability and the probability of an uncertain reward are distinctly encoded as entropy and a distorted probability weight, respectively, in the separate neural systems. However, previous behavioral economic and decision-theoretic models could not quantify reward-seeking and uncertainty aversion in a theoretically consistent manner. In this paper, we have: (i) proposed that generalized Helmholtz free energy in Tsallis’ non-extensive thermostatistics can be utilized to quantify a perceived value of an uncertain reward, and (ii) empirically examined the explanatory powers of the models. Future study directions in neuroeconomics and econophysics by utilizing the Tsallis’ free energy model are discussed.

Statistical mechanics of solitons

International Nuclear Information System (INIS)

Bishop, A.

1980-01-01

The status of statistical mechanics theory (classical and quantum, statics and dynamics) is reviewed for 1-D soliton or solitary-wave-bearing systems. Primary attention is given to (i) perspective for existing results with evaluation and representative literature guide; (ii) motivation and status report for remaining problems; (iii) discussion of connections with other 1-D topics

A non-extensive thermodynamic theory of ecological systems

Science.gov (United States)

Van Xuan, Le; Khac Ngoc, Nguyen; Lan, Nguyen Tri; Viet, Nguyen Ai

2017-06-01

After almost 30 years of development, it is not controversial issue that the so-called Tsallis entropy provides a useful approach to studying the complexity where the non-additivity of the systems under consideration is frequently met. Also, in the ecological research, Tsallis entropy, or in other words, q-entropy has been found itself as a generalized approach to define a range of diversity indices including Shannon-Wiener and Simpson indices. As a further stage of development in theoretical research, a thermodynamic theory based on Tsallis entropy or diversity indices in ecology has to be constructed for ecological systems to provide knowledge of ecological macroscopic behaviors. The standard method of theoretical physics is used in the manipulation and the equivalence between phenomenological thermodynamics and ecological aspects is the purpose of the ongoing research. The present work is in the line of the authors research to implement Tsallis non-extensivity approach to obtain the most important thermodynamic quantities of ecological systems such as internal energy Uq and temperature Tq based on a given modeled truncated Boltzmann distribution of the Whittaker plot for a dataset. These quantities have their own ecological meaning, especially the temperature Tq provides the insight of equilibrium condition among ecological systems as it is well-known in 0th law of thermodynamics.

Statistical ensembles in quantum mechanics

International Nuclear Information System (INIS)

Blokhintsev, D.

1976-01-01

The interpretation of quantum mechanics presented in this paper is based on the concept of quantum ensembles. This concept differs essentially from the canonical one by that the interference of the observer into the state of a microscopic system is of no greater importance than in any other field of physics. Owing to this fact, the laws established by quantum mechanics are not of less objective character than the laws governing classical statistical mechanics. The paradoxical nature of some statements of quantum mechanics which result from the interpretation of the wave functions as the observer's notebook greatly stimulated the development of the idea presented. (Auth.)

Statistical Mechanics of Prion Diseases

International Nuclear Information System (INIS)

Slepoy, A.; Singh, R. R. P.; Pazmandi, F.; Kulkarni, R. V.; Cox, D. L.

2001-01-01

We present a two-dimensional, lattice based, protein-level statistical mechanical model for prion diseases (e.g., mad cow disease) with concomitant prion protein misfolding and aggregation. Our studies lead us to the hypothesis that the observed broad incubation time distribution in epidemiological data reflect fluctuation dominated growth seeded by a few nanometer scale aggregates, while much narrower incubation time distributions for innoculated lab animals arise from statistical self-averaging. We model ''species barriers'' to prion infection and assess a related treatment protocol

Fractional Laplace Transforms - A Perspective

Directory of Open Access Journals (Sweden)

Rudolf A. Treumann

2014-06-01

Full Text Available A new form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral equations or problems in non-extensive statistical mechanics.

Towards a large deviation theory for strongly correlated systems

International Nuclear Information System (INIS)

Ruiz, Guiomar; Tsallis, Constantino

2012-01-01

A large-deviation connection of statistical mechanics is provided by N independent binary variables, the (N→∞) limit yielding Gaussian distributions. The probability of n≠N/2 out of N throws is governed by e −Nr , r related to the entropy. Large deviations for a strong correlated model characterized by indices (Q,γ) are studied, the (N→∞) limit yielding Q-Gaussians (Q→1 recovers a Gaussian). Its large deviations are governed by e q −Nr q (∝1/N 1/(q−1) , q>1), q=(Q−1)/(γ[3−Q])+1. This illustration opens the door towards a large-deviation foundation of nonextensive statistical mechanics. -- Highlights: ► We introduce the formalism of relative entropy for a single random binary variable and its q-generalization. ► We study a model of N strongly correlated binary random variables and their large-deviation probabilities. ► Large-deviation probability of strongly correlated model exhibits a q-exponential decay whose argument is proportional to N, as extensivity requires. ► Our results point to a q-generalized large deviation theory and suggest a large-deviation foundation of nonextensive statistical mechanics.

Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

International Nuclear Information System (INIS)

Remler, E.A.

1977-01-01

A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

The nonextensive parameter for nonequilibrium electron gas in an electromagnetic field

International Nuclear Information System (INIS)

Yu, Haining; Du, Jiulin

2014-01-01

The nonextensive parameter for nonequilibrium electron gas of the plasma in an electromagnetic field is studied. We exactly obtained an expression of the q-parameter based on Boltzmann kinetic theories for plasmas, where Coulombian interactions and Lorentz forces play dominant roles. We show that the q-parameter different from unity is related by an equation to temperature gradient, electric field strength, magnetic induction as well as overall bulk velocity of the gas. The effect of the magnetic field on the q-parameter depends on the overall bulk velocity. Thus the q-parameter for the electron gas in an electromagnetic field represents the nonequilibrium nature or nonisothermal configurations of the plasma with electromagnetic interactions. - Highlights: • An expression of the q-parameter is obtained for nonequilibrium plasma with electromagnetic interactions. • The q-parameter is related to temperature gradient, electric field strength, magnetic induction as well as overall bulk velocity of the plasma. • The q-parameter represents the nonequilibrium nature of the complex plasma with electromagnetic interactions

The nonextensive parameter for nonequilibrium electron gas in an electromagnetic field

Energy Technology Data Exchange (ETDEWEB)

Yu, Haining; Du, Jiulin, E-mail: jldu@tju.edu.cn

2014-11-15

The nonextensive parameter for nonequilibrium electron gas of the plasma in an electromagnetic field is studied. We exactly obtained an expression of the q-parameter based on Boltzmann kinetic theories for plasmas, where Coulombian interactions and Lorentz forces play dominant roles. We show that the q-parameter different from unity is related by an equation to temperature gradient, electric field strength, magnetic induction as well as overall bulk velocity of the gas. The effect of the magnetic field on the q-parameter depends on the overall bulk velocity. Thus the q-parameter for the electron gas in an electromagnetic field represents the nonequilibrium nature or nonisothermal configurations of the plasma with electromagnetic interactions. - Highlights: • An expression of the q-parameter is obtained for nonequilibrium plasma with electromagnetic interactions. • The q-parameter is related to temperature gradient, electric field strength, magnetic induction as well as overall bulk velocity of the plasma. • The q-parameter represents the nonequilibrium nature of the complex plasma with electromagnetic interactions.

Zeno dynamics in quantum statistical mechanics

International Nuclear Information System (INIS)

Schmidt, Andreas U

2003-01-01

We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium

Journey Through Statistical Mechanics

Science.gov (United States)

Yang, C. N.

2013-05-01

My first involvement with statistical mechanics and the many body problem was when I was a student at The National Southwest Associated University in Kunming during the war. At that time Professor Wang Zhu-Xi had just come back from Cambridge, England, where he was a student of Fowler, and his thesis was on phase transitions, a hot topic at that time, and still a very hot topic today...

Statistical crack mechanics

International Nuclear Information System (INIS)

Dienes, J.K.

1993-01-01

Although it is possible to simulate the ground blast from a single explosive shot with a simple computer algorithm and appropriate constants, the most commonly used modelling methods do not account for major changes in geology or shot energy because mechanical features such as tectonic stresses, fault structure, microcracking, brittle-ductile transition, and water content are not represented in significant detail. An alternative approach for modelling called Statistical Crack Mechanics is presented in this paper. This method, developed in the seventies as a part of the oil shale program, accounts for crack opening, shear, growth, and coalescence. Numerous photographs and micrographs show that shocked materials tend to involve arrays of planar cracks. The approach described here provides a way to account for microstructure and give a representation of the physical behavior of a material at the microscopic level that can account for phenomena such as permeability, fragmentation, shear banding, and hot-spot formation in explosives

Statistical mechanics of black holes

International Nuclear Information System (INIS)

Harms, B.; Leblanc, Y.

1992-01-01

We analyze the statistical mechanics of a gas of neutral and charged black holes. The microcanonical ensemble is the only possible approach to this system, and the equilibrium configuration is the one for which most of the energy is carried by a single black hole. Schwarzschild black holes are found to obey the statistical bootstrap condition. In all cases, the microcanonical temperature is identical to the Hawking temperature of the most massive black hole in the gas. U(1) charges in general break the bootstrap property. The problems of black-hole decay and of quantum coherence are also addressed

Is there a statistical mechanics of turbulence?

International Nuclear Information System (INIS)

Kraichnan, R.H.; Chen, S.Y.

1988-09-01

The statistical-mechanical treatment of turbulence is made questionable by strong nonlinearity and strong disequilibrium that result in the creation of ordered structures imbedded in disorder. Model systems are described which may provide some hope that a compact, yet faithful, statistical description of turbulence nevertheless is possible. Some essential dynamic features of the models are captured by low-order statistical approximations despite strongly non-Gaussian behavior. 31 refs., 5 figs

Statistical mechanics of multipartite entanglement

Science.gov (United States)

Facchi, P.; Florio, G.; Marzolino, U.; Parisi, G.; Pascazio, S.

2009-02-01

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.

Statistical mechanics of multipartite entanglement

Energy Technology Data Exchange (ETDEWEB)

Facchi, P [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); Florio, G; Pascazio, S [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Marzolino, U [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Parisi, G [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185 Roma, Italy, Centre for Statistical Mechanics and Complexity (SMC), CNR-INFM, 00185 Roma (Italy)

2009-02-06

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.

Statistical mechanics of multipartite entanglement

International Nuclear Information System (INIS)

Facchi, P; Florio, G; Pascazio, S; Marzolino, U; Parisi, G

2009-01-01

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics

Statistical mechanics in the context of special relativity.

Science.gov (United States)

Kaniadakis, G

2002-11-01

In Ref. [Physica A 296, 405 (2001)], starting from the one parameter deformation of the exponential function exp(kappa)(x)=(sqrt[1+kappa(2)x(2)]+kappax)(1/kappa), a statistical mechanics has been constructed which reduces to the ordinary Boltzmann-Gibbs statistical mechanics as the deformation parameter kappa approaches to zero. The distribution f=exp(kappa)(-beta E+betamu) obtained within this statistical mechanics shows a power law tail and depends on the nonspecified parameter beta, containing all the information about the temperature of the system. On the other hand, the entropic form S(kappa)= integral d(3)p(c(kappa) f(1+kappa)+c(-kappa) f(1-kappa)), which after maximization produces the distribution f and reduces to the standard Boltzmann-Shannon entropy S0 as kappa-->0, contains the coefficient c(kappa) whose expression involves, beside the Boltzmann constant, another nonspecified parameter alpha. In the present effort we show that S(kappa) is the unique existing entropy obtained by a continuous deformation of S0 and preserving unaltered its fundamental properties of concavity, additivity, and extensivity. These properties of S(kappa) permit to determine unequivocally the values of the above mentioned parameters beta and alpha. Subsequently, we explain the origin of the deformation mechanism introduced by kappa and show that this deformation emerges naturally within the Einstein special relativity. Furthermore, we extend the theory in order to treat statistical systems in a time dependent and relativistic context. Then, we show that it is possible to determine in a self consistent scheme within the special relativity the values of the free parameter kappa which results to depend on the light speed c and reduces to zero as c--> infinity recovering in this way the ordinary statistical mechanics and thermodynamics. The statistical mechanics here presented, does not contain free parameters, preserves unaltered the mathematical and epistemological structure of

Statistical mechanics of low-density parity-check codes

Energy Technology Data Exchange (ETDEWEB)

Kabashima, Yoshiyuki [Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 2268502 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)

2004-02-13

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multi-spin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems. (topical review)

Statistical mechanics of low-density parity-check codes

International Nuclear Information System (INIS)

Kabashima, Yoshiyuki; Saad, David

2004-01-01

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multi-spin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems. (topical review)

Quantum mechanics as a natural generalization of classical statistical mechanics

International Nuclear Information System (INIS)

Xu Laizi; Qian Shangwu

1994-01-01

By comparison between equations of motion of geometrical optics (GO) and that of classical statistical mechanics (CSM), it is found that there should be an analogy between GO and CSM instead of GO and classical mechanics (CM). Furthermore, by comparison between the classical limit (CL) of quantum mechanics (QM) and CSM, the authors find that CL of QM is CSM not CM, hence they demonstrated that QM is a natural generalization of CSM instead of CM

A statistical mechanical approach to restricted integer partition functions

Science.gov (United States)

Zhou, Chi-Chun; Dai, Wu-Sheng

2018-05-01

The main aim of this paper is twofold: (1) suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions—a way of writing an integer as a sum of other integers under certain restrictions. In this approach, the generating function of restricted integer partition functions is constructed from the canonical partition functions of various quantum gases. (2) Introducing a new type of restricted integer partition functions corresponding to general statistics which is a generalization of Gentile statistics in statistical mechanics; many kinds of restricted integer partition functions are special cases of this restricted integer partition function. Moreover, with statistical mechanics as a bridge, we reveal a mathematical fact: the generating function of restricted integer partition function is just the symmetric function which is a class of functions being invariant under the action of permutation groups. Using this approach, we provide some expressions of restricted integer partition functions as examples.

Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics

Science.gov (United States)

He, Ping

2012-01-01

The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically symmetric collisionless self-gravitating systems. We use an approach that is very different from that of the conventional statistical mechanics of short-range interaction systems. We demonstrate that the equilibrium states of self-gravitating systems consist of both mechanical and statistical equilibria, with the former characterized by a series of velocity-moment equations and the latter by statistical equilibrium equations, which should be derived from the entropy principle. The velocity-moment equations of all orders are derived from the steady-state collisionless Boltzmann equation. We point out that the ergodicity is invalid for the whole self-gravitating system, but it can be re-established locally. Based on the local ergodicity, using Fermi-Dirac-like statistics, with the non-degenerate condition and the spatial independence of the local microstates, we rederive the Boltzmann-Gibbs entropy. This is consistent with the validity of the collisionless Boltzmann equation, and should be the correct entropy form for collisionless self-gravitating systems. Apart from the usual constraints of mass and energy conservation, we demonstrate that the series of moment or virialization equations must be included as additional constraints on the entropy functional when performing the variational calculus; this is an extension to the original prescription by White & Narayan. Any possible velocity distribution can be produced by the statistical-mechanical approach that we have developed with the extended Boltzmann-Gibbs/White-Narayan statistics. Finally, we discuss the questions of negative specific heat and ensemble inequivalence for self-gravitating systems.

Thermalized solutions, statistical mechanics and turbulence

Indian Academy of Sciences (India)

2015-02-20

Feb 20, 2015 ... In this study, we examine the intriguing connection between turbulence and equilibrium statistical mechanics. There are several recent works which emphasize this connection. Thus in the last ... Current Issue : Vol. 90, Issue 6.

Statistical mechanics and field theory

International Nuclear Information System (INIS)

Samuel, S.A.

1979-05-01

Field theory methods are applied to statistical mechanics. Statistical systems are related to fermionic-like field theories through a path integral representation. Considered are the Ising model, the free-fermion model, and close-packed dimer problems on various lattices. Graphical calculational techniques are developed. They are powerful and yield a simple procedure to compute the vacuum expectation value of an arbitrary product of Ising spin variables. From a field theorist's point of view, this is the simplest most logical derivation of the Ising model partition function and correlation functions. This work promises to open a new area of physics research when the methods are used to approximate unsolved problems. By the above methods a new model named the 128 pseudo-free vertex model is solved. Statistical mechanics intuition is applied to field theories. It is shown that certain relativistic field theories are equivalent to classical interacting gases. Using this analogy many results are obtained, particularly for the Sine-Gordon field theory. Quark confinement is considered. Although not a proof of confinement, a logical, esthetic, and simple picture is presented of how confinement works. A key ingredient is the insight gained by using an analog statistical system consisting of a gas of macromolecules. This analogy allows the computation of Wilson loops in the presence of topological vortices and when symmetry breakdown occurs in the topological quantum number. Topological symmetry breakdown calculations are placed on approximately the same level of rigor as instanton calculations. The picture of confinement that emerges is similar to the dual Meissner type advocated by Mandelstam. Before topological symmetry breakdown, QCD has monopoles bound linearly together by three topological strings. Topological symmetry breakdown corresponds to a new phase where these monopoles are liberated. It is these liberated monopoles that confine quarks. 64 references

Annotations to quantum statistical mechanics

CERN Document Server

Kim, In-Gee

2018-01-01

This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Baym’s lectures that were presented in the book Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Green’s functions in describing the properties of many-particle systems. The functions provided a method for discussing finite-temperature problems with no more conceptual difficulty than ground-state problems, and the method was equally applicable to boson and fermion systems and equilibrium and nonequilibrium problems. The lectures also explained nonequilibrium statistical physics in a systematic way and contained essential concepts on statistical physics in terms of Green’s functions with sufficient and rigorous details. In-Gee Kim thoroughly studied the lectures during one of his research projects but found that the unspecialized method used to present them in the form of a book reduced their readability. He st...

Applying Statistical Mechanics to pixel detectors

International Nuclear Information System (INIS)

Pindo, Massimiliano

2002-01-01

Pixel detectors, being made of a large number of active cells of the same kind, can be considered as significant sets to which Statistical Mechanics variables and methods can be applied. By properly redefining well known statistical parameters in order to let them match the ones that actually characterize pixel detectors, an analysis of the way they work can be performed in a totally new perspective. A deeper understanding of pixel detectors is attained, helping in the evaluation and comparison of their intrinsic characteristics and performance

Projection operator techniques in nonequilibrium statistical mechanics

International Nuclear Information System (INIS)

Grabert, H.

1982-01-01

This book is an introduction to the application of the projection operator technique to the statistical mechanics of irreversible processes. After a general introduction to the projection operator technique and statistical thermodynamics the Fokker-Planck and the master equation approach are described together with the response theory. Then, as applications the damped harmonic oscillator, simple fluids, and the spin relaxation are considered. (HSI)

Limiting processes in non-equilibrium classical statistical mechanics

International Nuclear Information System (INIS)

Jancel, R.

1983-01-01

After a recall of the basic principles of the statistical mechanics, the results of ergodic theory, the transient at the thermodynamic limit and his link with the transport theory near the equilibrium are analyzed. The fundamental problems put by the description of non-equilibrium macroscopic systems are investigated and the kinetic methods are stated. The problems of the non-equilibrium statistical mechanics are analyzed: irreversibility and coarse-graining, macroscopic variables and kinetic description, autonomous reduced descriptions, limit processes, BBGKY hierarchy, limit theorems [fr

Multiparticle quantum mechanics obeying fractional statistics

International Nuclear Information System (INIS)

Wu, Y.

1984-01-01

We obtain the rule governing many-body wave functions for particles obeying fractional statistics in two (space) dimensions. It generalizes and continuously interpolates the usual symmetrization and antisymmetrization. Quantum mechanics of more than two particles is discussed and some new features are found

Equilibrium statistical mechanics of lattice models

CERN Document Server

Lavis, David A

2015-01-01

Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg—Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi—Hijmans—De Boer hierarchy of approximations. In Part III the use of alge...

Bayesian approach to inverse statistical mechanics

Science.gov (United States)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Statistical mechanics of two-dimensional and geophysical flows

International Nuclear Information System (INIS)

Bouchet, Freddy; Venaille, Antoine

2012-01-01

The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter’s troposphere and ocean vortices and jets. Emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. After a brief presentation of the 2D Euler and quasi-geostrophic equations, the specificity of two-dimensional and geophysical turbulence is emphasized. The equilibrium microcanonical measure is built from the Liouville theorem. Important statistical mechanics concepts (large deviations and mean field approach) and thermodynamic concepts (ensemble inequivalence and negative heat capacity) are briefly explained and described. On this theoretical basis, we predict the output of the long time evolution of complex turbulent flows as statistical equilibria. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. A detailed comparison between these statistical equilibria and real flow observations is provided. We also present recent results for non-equilibrium situations, for the studies of either the relaxation towards equilibrium or non-equilibrium steady states. In this last case, forces and dissipation are in a statistical balance; fluxes of conserved quantity characterize the system and microcanonical or other equilibrium measures no longer describe the system.

The Dirac equation in classical statistical mechanics

International Nuclear Information System (INIS)

Ord, G.N.

2002-01-01

The Dirac equation, usually obtained by 'quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic continuation, making the model 'self-quantizing'. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum mechanics

Renyi statistics in equilibrium statistical mechanics

International Nuclear Information System (INIS)

Parvan, A.S.; Biro, T.S.

2010-01-01

The Renyi statistics in the canonical and microcanonical ensembles is examined both in general and in particular for the ideal gas. In the microcanonical ensemble the Renyi statistics is equivalent to the Boltzmann-Gibbs statistics. By the exact analytical results for the ideal gas, it is shown that in the canonical ensemble, taking the thermodynamic limit, the Renyi statistics is also equivalent to the Boltzmann-Gibbs statistics. Furthermore it satisfies the requirements of the equilibrium thermodynamics, i.e. the thermodynamical potential of the statistical ensemble is a homogeneous function of first degree of its extensive variables of state. We conclude that the Renyi statistics arrives at the same thermodynamical relations, as those stemming from the Boltzmann-Gibbs statistics in this limit.

Cellular automata and statistical mechanical models

International Nuclear Information System (INIS)

Rujan, P.

1987-01-01

The authors elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata. Transient and stationary properties of probabilistic automata are linked to surface and bulk properties, respectively, of restricted statistical mechanical systems. It is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata. Some exact results are derived, including duality transformations, exact mappings, disorder, and linear solutions. Many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties. This approach is considered to be a first step toward the design of fully parallel, probabilistic systems whose computational abilities rely on the cooperative behavior of their components

Mathematical methods in quantum and statistical mechanics

International Nuclear Information System (INIS)

Fishman, L.

1977-01-01

The mathematical structure and closed-form solutions pertaining to several physical problems in quantum and statistical mechanics are examined in some detail. The J-matrix method, introduced previously for s-wave scattering and based upon well-established Hilbert Space theory and related generalized integral transformation techniques, is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L 2 ), Laguerre (Slater), and oscillator (Gaussian) basis sets. The theory of relaxation in statistical mechanics within the context of the theory of linear integro-differential equations of the Master Equation type and their corresponding Markov processes is examined. Several topics of a mathematical nature concerning various computational aspects of the L 2 approach to quantum scattering theory are discussed

Introductory statistical mechanics for electron storage rings

International Nuclear Information System (INIS)

Jowett, J.M.

1986-07-01

These lectures introduce the beam dynamics of electron-positron storage rings with particular emphasis on the effects due to synchrotron radiation. They differ from most other introductions in their systematic use of the physical principles and mathematical techniques of the non-equilibrium statistical mechanics of fluctuating dynamical systems. A self-contained exposition of the necessary topics from this field is included. Throughout the development, a Hamiltonian description of the effects of the externally applied fields is maintained in order to preserve the links with other lectures on beam dynamics and to show clearly the extent to which electron dynamics in non-Hamiltonian. The statistical mechanical framework is extended to a discussion of the conceptual foundations of the treatment of collective effects through the Vlasov equation

Statistical algebraic approach to quantum mechanics

International Nuclear Information System (INIS)

Slavnov, D.A.

2001-01-01

The scheme for plotting the quantum theory with application of the statistical algebraic approach is proposed. The noncommutative algebra elements (observed ones) and nonlinear functionals on this algebra (physical state) are used as the primary constituents. The latter ones are associated with the single-unit measurement results. Certain physical state groups are proposed to consider as quantum states of the standard quantum mechanics. It is shown that the mathematical apparatus of the standard quantum mechanics may be reproduced in such a scheme in full volume [ru

Generalized Statistical Mechanics at the Onset of Chaos

Directory of Open Access Journals (Sweden)

Alberto Robledo

2013-11-01

Full Text Available Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gibbs (BG statistical mechanics has suggested the potential verification of these generalizations at the onset of chaos, when the only Lyapunov exponent vanishes and ergodic and mixing properties cease to hold. There are three well-known routes to chaos in these deterministic dissipative systems, period-doubling, quasi-periodicity and intermittency, which provide the setting in which to explore the limit of validity of the standard BG structure. It has been shown that there is a rich and intricate behavior for both the dynamics within and towards the attractors at the onset of chaos and that these two kinds of properties are linked via generalized statistical-mechanical expressions. Amongst the topics presented are: (i permanently growing sensitivity fluctuations and their infinite family of generalized Pesin identities; (ii the emergence of statistical-mechanical structures in the dynamics along the routes to chaos; (iii dynamical hierarchies with modular organization; and (iv limit distributions of sums of deterministic variables. The occurrence of generalized entropy properties in condensed-matter physical systems is illustrated by considering critical fluctuations, localization transition and glass formation. We complete our presentation with the description of the manifestations of the dynamics at the transitions to chaos in various kinds of complex systems, such as, frequency and size rank distributions and complex network images of time series. We discuss the results.

Statistical-mechanical formulation of Lyapunov exponents

International Nuclear Information System (INIS)

Tanase-Nicola, Sorin; Kurchan, Jorge

2003-01-01

We show how the Lyapunov exponents of a dynamic system can, in general, be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive concepts and techniques of approximation can hence be borrowed

(ajst) statistical mechanics model for orientational

African Journals Online (AJOL)

Science and Engineering Series Vol. 6, No. 2, pp. 94 - 101. STATISTICAL MECHANICS MODEL FOR ORIENTATIONAL. MOTION OF TWO-DIMENSIONAL RIGID ROTATOR. Malo, J.O. ... there is no translational motion and that they are well separated so .... constant and I is the moment of inertia of a linear rotator. Thus, the ...

Statistical mechanics and Lorentz violation

International Nuclear Information System (INIS)

Colladay, Don; McDonald, Patrick

2004-01-01

The theory of statistical mechanics is studied in the presence of Lorentz-violating background fields. The analysis is performed using the Standard-Model Extension (SME) together with a Jaynesian formulation of statistical inference. Conventional laws of thermodynamics are obtained in the presence of a perturbed hamiltonian that contains the Lorentz-violating terms. As an example, properties of the nonrelativistic ideal gas are calculated in detail. To lowest order in Lorentz violation, the scalar thermodynamic variables are only corrected by a rotationally invariant combination of parameters that mimics a (frame dependent) effective mass. Spin-couplings can induce a temperature-independent polarization in the classical gas that is not present in the conventional case. Precision measurements in the residual expectation values of the magnetic moment of Fermi gases in the limit of high temperature may provide interesting limits on these parameters

Statistical mechanics of complex networks

CERN Document Server

Rubi, Miguel; Diaz-Guilera, Albert

2003-01-01

Networks can provide a useful model and graphic image useful for the description of a wide variety of web-like structures in the physical and man-made realms, e.g. protein networks, food webs and the Internet. The contributions gathered in the present volume provide both an introduction to, and an overview of, the multifaceted phenomenology of complex networks. Statistical Mechanics of Complex Networks also provides a state-of-the-art picture of current theoretical methods and approaches.

Science Academies' Refresher Course in Statistical Mechanics

Indian Academy of Sciences (India)

2018-02-27

Feb 27, 2018 ... Post Graduate and Research Department of Physics. Bishop Moore ... The Course will cover the basic and advanced topics of Statistical. Mechanics ... Courses of good standing for promotion, vide notification. F3-1/2009 ...

Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

Science.gov (United States)

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

Exactly soluble problems in statistical mechanics

International Nuclear Information System (INIS)

Yang, C.N.

1983-01-01

In the last few years, a number of two-dimensional classical and one-dimensional quantum mechanical problems in statistical mechanics have been exactly solved. Although these problems range over models of diverse physical interest, their solutions were obtained using very similar mathematical methods. In these lectures, the main points of the methods are discussed. In this introductory lecture, an overall survey of all these problems without going into the detailed method of solution is given. In later lectures, they shall concentrate on one particular problem: the delta function interaction in one dimension, and go into the details of that problem

Principles of classical statistical mechanics: A perspective from the notion of complementarity

International Nuclear Information System (INIS)

Velazquez Abad, Luisberis

2012-01-01

Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the complementarity between two descriptions that are unified in thermodynamics: (i) the parametrization of the system macrostate in terms of mechanical macroscopic observablesI=(I i ), and (ii) the dynamical description that explains the evolution of a system towards the thermodynamic equilibrium. As expected, such a complementarity is related to the uncertainty relations of classical statistical mechanics ΔI i Δη i ≥k. Here, k is the Boltzmann constant, η i =∂S(I|θ)/∂I i are the restituting generalized forces derived from the entropy S(I|θ) of a closed system, which is found in an equilibrium situation driven by certain control parameters θ=(θ α ). These arguments constitute the central ingredients of a reformulation of classical statistical mechanics from the notion of complementarity. In this new framework, Einstein postulate of classical fluctuation theory dp(I|θ)∼exp[S(I|θ)/k]dI appears as the correspondence principle between classical statistical mechanics and thermodynamics in the limit k→0, while the existence of uncertainty relations can be associated with the non-commuting character of certain operators. - Highlights: ► There exists a direct analogy between quantum and classical statistical mechanics. ► Statistical form of Le Chatellier principle leads to the uncertainty principle. ► Einstein postulate is simply the correspondence principle. ► Complementary quantities are associated with non-commuting operators.

On the putative essential discreteness of q-generalized entropies

Science.gov (United States)

Plastino, A.; Rocca, M. C.

2017-12-01

It has been argued in Abe (2010), entitled Essential discreteness in generalized thermostatistics with non-logarithmic entropy, that ;continuous Hamiltonian systems with long-range interactions and the so-called q-Gaussian momentum distributions are seen to be outside the scope of non-extensive statistical mechanics;. The arguments are clever and appealing. We show here that, however, some mathematical subtleties render them unconvincing.

Statistical mechanics for a system with imperfections: pt. 1

International Nuclear Information System (INIS)

Choh, S.T.; Kahng, W.H.; Um, C.I.

1982-01-01

Statistical mechanics is extended to treat a system where parts of the Hamiltonian are randomly varying. As the starting point of the theory, the statistical correlation among energy levels is neglected, allowing use of the central limit theorem of the probability theory. (Author)

Introduction to quantum statistical mechanics

CERN Document Server

Bogolyubov, N N

2010-01-01

Introduction to Quantum Statistical Mechanics (Second Edition) may be used as an advanced textbook by graduate students, even ambitious undergraduates in physics. It is also suitable for non experts in physics who wish to have an overview of some of the classic and fundamental quantum models in the subject. The explanation in the book is detailed enough to capture the interest of the reader, and complete enough to provide the necessary background material needed to dwell further into the subject and explore the research literature.

Quantum mechanics and field theory with fractional spin and statistics

International Nuclear Information System (INIS)

Forte, S.

1992-01-01

Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed

An introduction to statistical mechanics and thermodynamics

CERN Document Server

Swendsen, Robert H

2012-01-01

This text presents the two complementary aspects of thermal physics as an integrated theory of the properties of matter. Conceptual understanding is promoted by thorough development of basic concepts. In contrast to many texts, statistical mechanics, including discussion of the required probability theory, is presented first. This provides a statistical foundation for the concept of entropy, which is central to thermal physics. A unique feature of the book is the development ofentropy based on Boltzmann's 1877 definition; this avoids contradictions or ad hoc corrections found in other texts. D

Statistical mechanics of violent relaxation

International Nuclear Information System (INIS)

Shu, F.H.

1978-01-01

We reexamine the foundations of Lynden-Bell's statistical mechanical discussion of violent relaxation in collisionless stellar systems. We argue that Lynden-Bell's formulation in terms of a continuum description introduces unnecessary complications, and we consider a more conventional formulation in terms of particles. We then find the exclusion principle discovered by Lynden-Bell to be quantitatively important only at phase densities where two-body encounters are no longer negligible. Since the edynamical basis for the exclusion principle vanishes in such cases anyway, Lynden-Bell statistics always reduces in practice to Maxwell-Boltzmann statistics when applied to stellar systems. Lynden-Bell also found the equilibrium distribution function generally to be a sum of Maxwellians with velocity dispersions dependent on the phase density at star formation. We show that this difficulty vanishes in the particulate description for an encounterless stellar system as long as stars of different masses are initially well mixed in phase space. Our methods also demonstrate the equivalence between Gibbs's formalism which uses the microcanonical ensemble and Boltzmann's formalism which uses a coarse-grained continuum description. In addition, we clarify the concept of irreversible behavior on a macroscopic scale for an encounterless stellar system. Finally, we comment on the use of unusual macroscopic constraints to simulate the effects of incomplete relaxation

The road to Maxwell's demon conceptual foundations of statistical mechanics

CERN Document Server

Hemmo, Meir

2012-01-01

Time asymmetric phenomena are successfully predicted by statistical mechanics. Yet the foundations of this theory are surprisingly shaky. Its explanation for the ease of mixing milk with coffee is incomplete, and even implies that un-mixing them should be just as easy. In this book the authors develop a new conceptual foundation for statistical mechanics that addresses this difficulty. Explaining the notions of macrostates, probability, measurement, memory, and the arrow of time in statistical mechanics, they reach the startling conclusion that Maxwell's Demon, the famous perpetuum mobile, is consistent with the fundamental physical laws. Mathematical treatments are avoided where possible, and instead the authors use novel diagrams to illustrate the text. This is a fascinating book for graduate students and researchers interested in the foundations and philosophy of physics.

Statistical mechanics of cellular automata

International Nuclear Information System (INIS)

Wolfram, S.

1983-01-01

Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions approx. =1.59 or approx. =1.69. With ''random'' initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed

Statistical mechanics of systems of unbounded spins

Energy Technology Data Exchange (ETDEWEB)

Lebowitz, J L [Yeshiva Univ., New York (USA). Belfer Graduate School of Science; Presutti, E [L' Aquila Univ. (Italy). Istituto di Matematica

1976-11-01

We develop the statistical mechanics of unbounded n-component spin systems interacting via potentials which are superstable and strongly tempered. The uniqueness of the equilibrium state is then proven for one component ferromagnetic spins whose free energy is differentiable with respect to the magnetic field.

Noisy coupled logistic maps in the vicinity of chaos threshold.

Science.gov (United States)

Tirnakli, Ugur; Tsallis, Constantino

2016-04-01

We focus on a linear chain of N first-neighbor-coupled logistic maps in the vicinity of their edge of chaos in the presence of a common noise. This model, characterised by the coupling strength ϵ and the noise width σmax, was recently introduced by Pluchino et al. [Phys. Rev. E 87, 022910 (2013)]. They detected, for the time averaged returns with characteristic return time τ, possible connections with q-Gaussians, the distributions which optimise, under appropriate constraints, the nonadditive entropy, Sq, basis of nonextensive statistics mechanics. Here, we take a closer look on this model, and numerically obtain probability distributions which exhibit a slight asymmetry for some parameter values, in variance with simple q-Gaussians. Nevertheless, along many decades, the fitting with q-Gaussians turns out to be numerically very satisfactory for wide regions of the parameter values, and we illustrate how the index q evolves with (N,τ,ϵ,σmax). It is nevertheless instructive on how careful one must be in such numerical analysis. The overall work shows that physical and/or biological systems that are correctly mimicked by this model are thermostatistically related to nonextensive statistical mechanics when time-averaged relevant quantities are studied.

Fluctuations of physical values in statistical mechanics

International Nuclear Information System (INIS)

Zaripov, R.G.

1999-01-01

The new matrix inequalities for the boundary of measurement accuracy of physical values in the ensemble of quantum systems were obtained. The multidimensional thermodynamical parameter measurement is estimated. The matrix inequalities obtained are quantum analogs of the Cramer-Rao information inequalities in mathematical statistics. The quantity of information in quantum mechanical measurement, connected with the boundaries of jointly measurable values in one macroscopic experiment was determined. The lower boundary of the variance of estimation of multidimensional quantum mechanical parameter was found. (author)

Fundamental link between system theory and statistical mechanics

International Nuclear Information System (INIS)

Atmanspacher, H.; Scheingraber, H.

1987-01-01

A fundamental link between system theory and statistical mechanics has been found to be established by the Kolmogorov entropy. By this quantity the temporal evolution of dynamical systems can be classified into regular, chaotic, and stochastic processes. Since K represents a measure for the internal information creation rate of dynamical systems, it provides an approach to irreversibility. The formal relationship to statistical mechanics is derived by means of an operator formalism originally introduced by Prigogine. For a Liouville operator L and an information operator M tilde acting on a distribution in phase space, it is shown that i[L, M tilde] = KI (I = identity operator). As a first consequence of this equivalence, a relation is obtained between the chaotic correlation time of a system and Prigogine's concept of a finite duration of presence. Finally, the existence of chaos in quantum systems is discussed with respect to the existence of a quantum mechanical time operator

Statistical mechanics and the description of the early universe II. Principle of detailed balance and primordial 4He formation

DEFF Research Database (Denmark)

Pessah, Martin Elias; F. Torres, Diego

2001-01-01

If the universe is slightly non-extensive, and the distribution functions are not exactly given by those of Boltzmann-Gibbs, the primordial production of light elements will be non-trivially modified. In particular, the principle of detailed balance (PDB), of fundamental importance in the standard...... the formation of Helium and Deuterium, and study the kind of deviation one could expect from the standard regime. The correction to the capture time, the moment in which Deuterium can no longer be substantially photo-disintegrated, is also presented. This allows us to take into account the process of the free...

Infinite Random Graphs as Statistical Mechanical Models

DEFF Research Database (Denmark)

Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria

2011-01-01

We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...

Statistical mechanics and the physics of fluids

CERN Document Server

Tosi, Mario

This volume collects the lecture notes of a course on statistical mechanics, held at Scuola Normale Superiore di Pisa for third-to-fifth year students in physics and chemistry. Three main themes are covered in the book. The first part gives a compact presentation of the foundations of statistical mechanics and their connections with thermodynamics. Applications to ideal gases of material particles and of excitation quanta are followed by a brief introduction to a real classical gas and to a weakly coupled classical plasma, and by a broad overview on the three states of matter.The second part is devoted to fluctuations around equilibrium and their correlations. Coverage of liquid structure and critical phenomena is followed by a discussion of irreversible processes as exemplified by diffusive motions and by the dynamics of density and heat fluctuations. Finally, the third part is an introduction to some advanced themes: supercooling and the glassy state, non-Newtonian fluids including polymers and liquid cryst...

Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions

International Nuclear Information System (INIS)

Ourabah, Kamel; Tribeche, Mouloud

2014-01-01

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q-statistics. Starting from the q-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy preserves a scaling property of this equation. The q-statistical approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q is traced. It is found that the q-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length. -- Highlights: •Thomas–Fermi approach for self-gravitating fermions. •A generalized Thomas–Fermi equation is derived. •Nonextensivity preserves a scaling property of this equation. •Nonextensive approach to Jeans’ instability of self-gravitating fermions. •It is found that nonextensivity makes the Fermionic system unstable at shorter scales

On the statistical-mechanical meaning of the Bousso bound

International Nuclear Information System (INIS)

Pesci, Alessandro

2008-01-01

The Bousso entropy bound, in its generalized form, is investigated for the case of perfect fluids at local thermodynamic equilibrium and evidence is found that the bound is satisfied if and only if a certain local thermodynamic property holds, emerging when the attempt is made to apply the bound to thin layers of matter. This property consists of the existence of an ultimate lower limit l* to the thickness of the slices for which a statistical-mechanical description is viable, depending l* on the thermodynamical variables which define the state of the system locally. This limiting scale, found to be in general much larger than the Planck scale (so that no Planck scale physics must be necessarily invoked to justify it), appears not related to gravity and this suggests that the generalized entropy bound is likely to be rooted on conventional flat-spacetime statistical mechanics, with the maximum admitted entropy being however actually determined also by gravity. Some examples of ideal fluids are considered in order to identify the mechanisms which can set a lower limit to the statistical-mechanical description and these systems are found to respect the lower limiting scale l*. The photon gas, in particular, appears to seemingly saturate this limiting scale and the consequence is drawn that for systems consisting of a single slice of a photon gas with thickness l*, the generalized Bousso bound is saturated. It is argued that this seems to open the way to a peculiar understanding of black hole entropy: if an entropy can meaningfully (i.e. with a second law) be assigned to a black hole, the value A/4 for it (where A is the area of the black hole) is required simply by (conventional) statistical mechanics coupled to general relativity

Statistical Mechanics of Disordered Systems - Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 18)

Science.gov (United States)

Bovier, Anton

2006-06-01

Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail. Comprehensive introduction to an active and fascinating area of research Clear exposition that builds to the state of the art in the mathematics of spin glasses Written by a well-known and active researcher in the field

Statistical mechanics and the foundations of thermodynamics

International Nuclear Information System (INIS)

Loef, A.M.

1979-01-01

An introduction to classical statistical mechanics and its relation to thermodynamics is presented. Emphasis is put on getting a detailed and logical presentation of the foundations of thermodynamics based on the maximum entropy principles which govern the values taken by macroscopic variables according to the laws of large numbers

Statistical fracture mechanics approach to the strength of brittle rock

International Nuclear Information System (INIS)

Ratigan, J.L.

1981-06-01

Statistical fracture mechanics concepts used in the past for rock are critically reviewed and modifications are proposed which are warranted by (1) increased understanding of fracture provided by modern fracture mechanics and (2) laboratory test data both from the literature and from this research. Over 600 direct and indirect tension tests have been performed on three different rock types; Stripa Granite, Sierra White Granite and Carrara Marble. In several instances assumptions which are common in the literature were found to be invalid. A three parameter statistical fracture mechanics model with Mode I critical strain energy release rate as the variant is presented. Methodologies for evaluating the parameters in this model as well as the more commonly employed two parameter models are discussed. The experimental results and analysis of this research indicate that surfacially distributed flaws, rather than volumetrically distributed flaws are responsible for rupture in many testing situations. For several of the rock types tested, anisotropy (both in apparent tensile strength and size effect) precludes the use of contemporary statistical fracture mechanics models

Stability and equilibrium in quantum statistical mechanics

International Nuclear Information System (INIS)

Kastler, Daniel.

1975-01-01

A derivation of the Gibbs Ansatz, base of the equilibrium statistical mechanics is provided from a stability requirements, in technical connection with the harmonic analysis of non-commutative dynamical systems. By the same token a relation is established between stability and the positivity of Hamiltonian in the zero temperature case [fr

Statistical mechanics of budget-constrained auctions

OpenAIRE

Altarelli, F.; Braunstein, A.; Realpe-Gomez, J.; Zecchina, R.

2009-01-01

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). Based on the cavity method of statistical mechanics, we introduce a message passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution,...

Statistical mechanics of the vertex-cover problem

Science.gov (United States)

Hartmann, Alexander K.; Weigt, Martin

2003-10-01

We review recent progress in the study of the vertex-cover problem (VC). The VC belongs to the class of NP-complete graph theoretical problems, which plays a central role in theoretical computer science. On ensembles of random graphs, VC exhibits a coverable-uncoverable phase transition. Very close to this transition, depending on the solution algorithm, easy-hard transitions in the typical running time of the algorithms occur. We explain a statistical mechanics approach, which works by mapping the VC to a hard-core lattice gas, and then applying techniques such as the replica trick or the cavity approach. Using these methods, the phase diagram of the VC could be obtained exactly for connectivities c e, the solution of the VC exhibits full replica symmetry breaking. The statistical mechanics approach can also be used to study analytically the typical running time of simple complete and incomplete algorithms for the VC. Finally, we describe recent results for the VC when studied on other ensembles of finite- and infinite-dimensional graphs.

Statistical mechanics of the vertex-cover problem

International Nuclear Information System (INIS)

Hartmann, Alexander K; Weigt, Martin

2003-01-01

We review recent progress in the study of the vertex-cover problem (VC). The VC belongs to the class of NP-complete graph theoretical problems, which plays a central role in theoretical computer science. On ensembles of random graphs, VC exhibits a coverable-uncoverable phase transition. Very close to this transition, depending on the solution algorithm, easy-hard transitions in the typical running time of the algorithms occur. We explain a statistical mechanics approach, which works by mapping the VC to a hard-core lattice gas, and then applying techniques such as the replica trick or the cavity approach. Using these methods, the phase diagram of the VC could be obtained exactly for connectivities c e, the solution of the VC exhibits full replica symmetry breaking. The statistical mechanics approach can also be used to study analytically the typical running time of simple complete and incomplete algorithms for the VC. Finally, we describe recent results for the VC when studied on other ensembles of finite- and infinite-dimensional graphs

Statistical Mechanics and Black Hole Thermodynamics

OpenAIRE

Carlip, Steven

1997-01-01

Black holes are thermodynamic objects, but despite recent progress, the ultimate statistical mechanical origin of black hole temperature and entropy remains mysterious. Here I summarize an approach in which the entropy is viewed as arising from ``would-be pure gauge'' degrees of freedom that become dynamical at the horizon. For the (2+1)-dimensional black hole, these degrees of freedom can be counted, and yield the correct Bekenstein-Hawking entropy; the corresponding problem in 3+1 dimension...

Mathematics of statistical mechanics and the chaos theory

International Nuclear Information System (INIS)

Llave, R. de la; Haro, A.

2000-01-01

Statistical mechanics requires a language that unifies probabilistic and deterministic description of physical systems. We describe briefly some of the mathematical ideas needed for this unification. These ideas have also proved important in the study of chaotic systems. (Author) 17 refs

Brief introduction to Lie-admissible formulations in statistical mechanics

International Nuclear Information System (INIS)

Fronteau, J.

1981-01-01

The present article is a summary of the essential ideas and results published in previous articles, the aim here being to describe the situation in a schematic way for the benefit of non-specialists. The non-truncated Liouville theorem and equation, natural introduction of Lie-admissible formulations into statistical mechanics, the notion of a statistical quasi-particle, and transition towards the notion of fine thermodynamics are discussed

The p-sphere and the geometric substratum of power-law probability distributions

International Nuclear Information System (INIS)

Vignat, C.; Plastino, A.

2005-01-01

Links between power law probability distributions and marginal distributions of uniform laws on p-spheres in R n show that a mathematical derivation of the Boltzmann-Gibbs distribution necessarily passes through power law ones. Results are also given that link parameters p and n to the value of the non-extensivity parameter q that characterizes these power laws in the context of non-extensive statistics

Statistical mechanics of the majority game

International Nuclear Information System (INIS)

Kozlowski, P; Marsili, M

2003-01-01

The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfield-like Hamiltonian. On the basis of replica symmetric calculations, we draw the phase diagram, which contains the analogue of a retrieval phase. The number of metastable states is estimated using the annealed approximation. The results are confronted with extensive numerical simulations

Statistical mechanics of directed models of polymers in the square lattice

CERN Document Server

Rensburg, J V

2003-01-01

Directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature. These are idealized geometric directed lattice models introduced to study phase behaviour in polymers, and include Dyck paths, partially directed paths, directed trees and directed vesicles models. Directed models are closely related to models studied in the combinatorics literature (and are often exactly solvable). They are also simplified versions of a number of statistical mechanics models, including the self-avoiding walk, lattice animals and lattice vesicles. The exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models, and this will be explored in this review. The combinatorial nature of directed lattice path models makes a study using generating function approaches most natural. In contrast, the statistical mechanics approach would introduce...

Quantum field theory and statistical mechanics

International Nuclear Information System (INIS)

Jegerlehner, F.

1975-01-01

At first a heuristic understanding is given how the relation between quantum field theory and statistical mechanics near phase transitions comes about. A long range scale invariant theory is constructed, critical indices are calculated and the relations among them are proved, field theoretical Kadanoff-scale transformations are formulated and scaling corrections calculated. A precise meaning to many of Kadanoffs considerations and a model matching Wegners phenomenological scheme is given. It is shown, that soft parametrization is most transparent for the discussion of scaling behaviour. (BJ) [de

Statistical Mechanics of Turbulent Dynamos

Science.gov (United States)

Shebalin, John V.

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much

Statistical mechanics of program systems

International Nuclear Information System (INIS)

Neirotti, Juan P; Caticha, Nestor

2006-01-01

We discuss the collective behaviour of a set of operators and variables that constitute a program and the emergence of meaningful computational properties in the language of statistical mechanics. This is done by appropriately modifying available Monte Carlo methods to deal with hierarchical structures. The study suggests, in analogy with simulated annealing, a method to automatically design programs. Reasonable solutions can be found, at low temperatures, when the method is applied to simple toy problems such as finding an algorithm that determines the roots of a function or one that makes a nonlinear regression. Peaks in the specific heat are interpreted as signalling phase transitions which separate regions where different algorithmic strategies are used to solve the problem

Metastability in Field Theory and Statistical Mechanics

International Nuclear Information System (INIS)

Carvalho, C.A. de.

1984-01-01

After a phase transition analysis which can occur in the framework of a scalar field theory, at finite temperature and in presence of a external field, possibles metastable situations are studied and also how is their relationship with the transitions. In both cases it is used a semiclassical approximation to the theory which, in Statistical Mechanics, corresponds to the droplet-bubble model. (L.C.) [pt

The statistical mechanics of learning a rule

International Nuclear Information System (INIS)

Watkin, T.L.H.; Rau, A.; Biehl, M.

1993-01-01

A summary is presented of the statistical mechanical theory of learning a rule with a neural network, a rapidly advancing area which is closely related to other inverse problems frequently encountered by physicists. By emphasizing the relationship between neural networks and strongly interacting physical systems, such as spin glasses, the authors show how learning theory has provided a workshop in which to develop new, exact analytical techniques

Thermodynamics and relativistic kinetic theory for q-generalized Bose-Einstein and Fermi-Dirac systems

Science.gov (United States)

Mitra, Sukanya

2018-01-01

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark-gluon system.

Principles of thermodynamics and statistical mechanics

CERN Document Server

Lawden, D F

2005-01-01

A thorough exploration of the universal principles of thermodynamics and statistical mechanics, this volume explains the applications of these essential rules to a multitude of situations arising in physics and engineering. It develops their use in a variety of circumstances-including those involving gases, crystals, and magnets-in order to illustrate general methods of analysis and to provide readers with all the necessary background to continue in greater depth with specific topics.Author D. F. Lawden has considerable experience in teaching this subject to university students of varied abili

Braid group, knot theory and statistical mechanics II

CERN Document Server

Yang Chen Ning

1994-01-01

The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors.

Statistical Mechanics of Turbulent Flows

International Nuclear Information System (INIS)

Cambon, C

2004-01-01

This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their

Statistical mechanics for a class of quantum statistics

International Nuclear Information System (INIS)

Isakov, S.B.

1994-01-01

Generalized statistical distributions for identical particles are introduced for the case where filling a single-particle quantum state by particles depends on filling states of different momenta. The system of one-dimensional bosons with a two-body potential that can be solved by means of the thermodynamic Bethe ansatz is shown to be equivalent thermodynamically to a system of free particles obeying statistical distributions of the above class. The quantum statistics arising in this way are completely determined by the two-particle scattering phases of the corresponding interacting systems. An equation determining the statistical distributions for these statistics is derived

Menzerath-Altmann Law: Statistical Mechanical Interpretation as Applied to a Linguistic Organization

Science.gov (United States)

Eroglu, Sertac

2014-10-01

The distribution behavior described by the empirical Menzerath-Altmann law is frequently encountered during the self-organization of linguistic and non-linguistic natural organizations at various structural levels. This study presents a statistical mechanical derivation of the law based on the analogy between the classical particles of a statistical mechanical organization and the distinct words of a textual organization. The derived model, a transformed (generalized) form of the Menzerath-Altmann model, was termed as the statistical mechanical Menzerath-Altmann model. The derived model allows interpreting the model parameters in terms of physical concepts. We also propose that many organizations presenting the Menzerath-Altmann law behavior, whether linguistic or not, can be methodically examined by the transformed distribution model through the properly defined structure-dependent parameter and the energy associated states.

Realistic thermodynamic and statistical-mechanical measures for neural synchronization.

Science.gov (United States)

Kim, Sang-Yoon; Lim, Woochang

2014-04-15

Synchronized brain rhythms, associated with diverse cognitive functions, have been observed in electrical recordings of brain activity. Neural synchronization may be well described by using the population-averaged global potential VG in computational neuroscience. The time-averaged fluctuation of VG plays the role of a "thermodynamic" order parameter O used for describing the synchrony-asynchrony transition in neural systems. Population spike synchronization may be well visualized in the raster plot of neural spikes. The degree of neural synchronization seen in the raster plot is well measured in terms of a "statistical-mechanical" spike-based measure Ms introduced by considering the occupation and the pacing patterns of spikes. The global potential VG is also used to give a reference global cycle for the calculation of Ms. Hence, VG becomes an important collective quantity because it is associated with calculation of both O and Ms. However, it is practically difficult to directly get VG in real experiments. To overcome this difficulty, instead of VG, we employ the instantaneous population spike rate (IPSR) which can be obtained in experiments, and develop realistic thermodynamic and statistical-mechanical measures, based on IPSR, to make practical characterization of the neural synchronization in both computational and experimental neuroscience. Particularly, more accurate characterization of weak sparse spike synchronization can be achieved in terms of realistic statistical-mechanical IPSR-based measure, in comparison with the conventional measure based on VG. Copyright © 2014. Published by Elsevier B.V.

Thermodynamics and statistical mechanics. [thermodynamic properties of gases

Science.gov (United States)

1976-01-01

The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping

Science.gov (United States)

Kubica, Aleksander; Beverland, Michael E.; Brandão, Fernando; Preskill, John; Svore, Krysta M.

2018-05-01

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p3DCC (1 )≃1.9 % and p3DCC (2 )≃27.6 % . We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Thermodynamics and relativistic kinetic theory for q-generalized Bose-Einstein and Fermi-Dirac systems

Energy Technology Data Exchange (ETDEWEB)

Mitra, Sukanya [Indian Institute of Technology Gandhinagar, Gandhinagar, Gujarat (India)

2018-01-15

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark-gluon system. (orig.)

Statistical mechanics of spatial evolutionary games

International Nuclear Information System (INIS)

Miekisz, Jacek

2004-01-01

We discuss the long-run behaviour of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash equilibria. We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We use concepts and techniques of statistical mechanics to study game-theoretic models. In order to obtain results in the case of the so-called potential games, we analyse the thermodynamic limit of the appropriate models of interacting particles

Early years of Computational Statistical Mechanics

Science.gov (United States)

Mareschal, Michel

2018-05-01

Evidence that a model of hard spheres exhibits a first-order solid-fluid phase transition was provided in the late fifties by two new numerical techniques known as Monte Carlo and Molecular Dynamics. This result can be considered as the starting point of computational statistical mechanics: at the time, it was a confirmation of a counter-intuitive (and controversial) theoretical prediction by J. Kirkwood. It necessitated an intensive collaboration between the Los Alamos team, with Bill Wood developing the Monte Carlo approach, and the Livermore group, where Berni Alder was inventing Molecular Dynamics. This article tells how it happened.

Molecular dynamics and Monte Carlo calculations in statistical mechanics

International Nuclear Information System (INIS)

Wood, W.W.; Erpenbeck, J.J.

1976-01-01

Monte Carlo and molecular dynamics calculations on statistical mechanical systems is reviewed giving some of the more significant recent developments. It is noted that the term molecular dynamics refers to the time-averaging technique for hard-core and square-well interactions and for continuous force-law interactions. Ergodic questions, methodology, quantum mechanical, Lorentz, and one-dimensional, hard-core, and square and triangular-well systems, short-range soft potentials, and other systems are included. 268 references

Representative volume size: A comparison of statistical continuum mechanics and statistical physics

Energy Technology Data Exchange (ETDEWEB)

AIDUN,JOHN B.; TRUCANO,TIMOTHY G.; LO,CHI S.; FYE,RICHARD M.

1999-05-01

In this combination background and position paper, the authors argue that careful work is needed to develop accurate methods for relating the results of fine-scale numerical simulations of material processes to meaningful values of macroscopic properties for use in constitutive models suitable for finite element solid mechanics simulations. To provide a definite context for this discussion, the problem is couched in terms of the lack of general objective criteria for identifying the size of the representative volume (RV) of a material. The objective of this report is to lay out at least the beginnings of an approach for applying results and methods from statistical physics to develop concepts and tools necessary for determining the RV size, as well as alternatives to RV volume-averaging for situations in which the RV is unmanageably large. The background necessary to understand the pertinent issues and statistical physics concepts is presented.

Introduction to nonequilibrium statistical mechanics with quantum field theory

International Nuclear Information System (INIS)

Kita, Takafumi

2010-01-01

In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (1) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (2) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (3) to derive an expression of nonequilibrium entropy that evolves with time. In stage (1), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Φ-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Φ-derivable approximation, i.e., an issue of how to handle the 'Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy'. Aim (2) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems can be handled microscopically with

Two-dimensional models in statistical mechanics and field theory

International Nuclear Information System (INIS)

Koberle, R.

1980-01-01

Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt

Is quantum theory a form of statistical mechanics?

Science.gov (United States)

Adler, S. L.

2007-05-01

We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantum mechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.

Statistical mechanical analysis of LMFBR fuel cladding tubes

International Nuclear Information System (INIS)

Poncelet, J.-P.; Pay, A.

1977-01-01

The most important design requirement on fuel pin cladding for LMFBR's is its mechanical integrity. Disruptive factors include internal pressure from mixed oxide fuel fission gas release, thermal stresses and high temperature creep, neutron-induced differential void-swelling as a source of stress in the cladding and irradiation creep of stainless steel material, corrosion by fission products. Under irradiation these load-restraining mechanisms are accentuated by stainless steel embrittlement and strength alterations. To account for the numerous uncertainties involved in the analysis by theoretical models and computer codes statistical tools are unavoidably requested, i.e. Monte Carlo simulation methods. Thanks to these techniques, uncertainties in nominal characteristics, material properties and environmental conditions can be linked up in a correct way and used for a more accurate conceptual design. First, a thermal creep damage index is set up through a sufficiently sophisticated clad physical analysis including arbitrary time dependence of power and neutron flux as well as effects of sodium temperature, burnup and steel mechanical behavior. Although this strain limit approach implies a more general but time consuming model., on the counterpart the net output is improved and e.g. clad temperature, stress and strain maxima may be easily assessed. A full spectrum of variables are statistically treated to account for their probability distributions. Creep damage probability may be obtained and can contribute to a quantitative fuel probability estimation

Statistical mechanics and the foundations of thermodynamics

International Nuclear Information System (INIS)

Martin-Loef, A.

1979-01-01

These lectures are designed as an introduction to classical statistical mechanics and its relation to thermodynamics. They are intended to bridge the gap between the treatment of the subject in physics text books and the modern presentations of mathematically rigorous results. We shall first introduce the probability distributions, ensembles, appropriate for describing systems in equilibrium and consider some of their basic physical applications. We also discuss the problem of approach to equilibrium and how irreversibility comes into the dynamics. We then give a detailed description of how the law of large numbers for macrovariables in equilibrium is derived from the fact that entropy is an extensive quantity in the thermodynamic limit. We show in a natural way how to split the energy changes in an thermodynamical process into work and heat leading to a derivation of the first and second laws of thermodynamics from the rules of thermodynamical equilibrium. We have elaborated this part in detail because we feel it is quite satisfactory, that the establishment of the limit of thermodynamic functions as achieved in the modern development of the mathematical aspects of statistical mechanics allows a more general and logically clearer presentation of the bases of thermodynamics. We close these lectures by presenting the basic facts about fluctuation theory. The treatment aims to be reasonably self-contained both concerning the physics and mathematics needed. No knowledge of quantum mechanics is presupposed. Since we spent a large part on mathematical proofs and give many technical facts these lectures are probably most digestive for the mathematically inclined reader who wants to understand the physics of the subject. (HJ)

Statistical mechanics and the evolution of polygenic quantitative traits

NARCIS (Netherlands)

Barton, N.H.; De Vladar, H.P.

The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified

STATISTICAL DISTRIBUTION PATTERNS IN MECHANICAL AND FATIGUE PROPERTIES OF METALLIC MATERIALS

OpenAIRE

Tatsuo, SAKAI; Masaki, NAKAJIMA; Keiro, TOKAJI; Norihiko, HASEGAWA; Department of Mechanical Engineering, Ritsumeikan University; Department of Mechanical Engineering, Toyota College of Technology; Department of Mechanical Engineering, Gifu University; Department of Mechanical Engineering, Gifu University

1997-01-01

Many papers on the statistical aspect of materials strength have been collected and reviewed by The Research Group for Statistical Aspects of Materials Strength.A book of "Statistical Aspects of Materials Strength" was written by this group, and published in 1992.Based on the experimental data compiled in this book, distribution patterns of mechanical properties are systematically surveyed paying an attention to metallic materials.Thus one can obtain the fundamental knowledge for a reliabilit...

Statistical physics of black holes as quantum-mechanical systems

OpenAIRE

Giddings, Steven B.

2013-01-01

Some basic features of black-hole statistical mechanics are investigated, assuming that black holes respect the principles of quantum mechanics. Care is needed in defining an entropy S_bh corresponding to the number of microstates of a black hole, given that the black hole interacts with its surroundings. An open question is then the relationship between this entropy and the Bekenstein-Hawking entropy S_BH. For a wide class of models with interactions needed to ensure unitary quantum evolutio...

A statistical mechanics approach to mixing in stratified fluids

OpenAIRE

Venaille , Antoine; Gostiaux , Louis; Sommeria , Joël

2016-01-01

Accepted for the Journal of Fluid Mechanics; Predicting how much mixing occurs when a given amount of energy is injected into a Boussinesq fluid is a longstanding problem in stratified turbulence. The huge number of degrees of freedom involved in these processes renders extremely difficult a deterministic approach to the problem. Here we present a statistical mechanics approach yielding a prediction for a cumulative, global mixing efficiency as a function of a global Richard-son number and th...

Topics in statistical mechanics

International Nuclear Information System (INIS)

Elser, V.

1984-05-01

This thesis deals with four independent topics in statistical mechanics: (1) the dimer problem is solved exactly for a hexagonal lattice with general boundary using a known generating function from the theory of partitions. It is shown that the leading term in the entropy depends on the shape of the boundary; (2) continuum models of percolation and self-avoiding walks are introduced with the property that their series expansions are sums over linear graphs with intrinsic combinatorial weights and explicit dimension dependence; (3) a constrained SOS model is used to describe the edge of a simple cubic crystal. Low and high temperature results are derived as well as the detailed behavior near the crystal facet; (4) the microscopic model of the lambda-transition involving atomic permutation cycles is reexamined. In particular, a new derivation of the two-component field theory model of the critical behavior is presented. Results for a lattice model originally proposed by Kikuchi are extended with a high temperature series expansion and Monte Carlo simulation. 30 references

Propagation of Electron Acoustic Soliton, Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

Science.gov (United States)

El-Hanbaly, A. M.; El-Shewy, E. K.; Elgarayhi, A.; Kassem, A. I.

2015-11-01

The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev-Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.

Classical statistical mechanics approach to multipartite entanglement

Energy Technology Data Exchange (ETDEWEB)

Facchi, P [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); Florio, G; Pascazio, S [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Marzolino, U [Dipartimento di Fisica, Universita di Trieste, and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34014 Trieste (Italy); Parisi, G [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, Centre for Statistical Mechanics and Complexity (SMC), CNR-INFM (Italy)

2010-06-04

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

Classical statistical mechanics approach to multipartite entanglement

Science.gov (United States)

Facchi, P.; Florio, G.; Marzolino, U.; Parisi, G.; Pascazio, S.

2010-06-01

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

Classical statistical mechanics approach to multipartite entanglement

International Nuclear Information System (INIS)

Facchi, P; Florio, G; Pascazio, S; Marzolino, U; Parisi, G

2010-01-01

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

A κ-generalized statistical mechanics approach to income analysis

Science.gov (United States)

Clementi, F.; Gallegati, M.; Kaniadakis, G.

2009-02-01

This paper proposes a statistical mechanics approach to the analysis of income distribution and inequality. A new distribution function, having its roots in the framework of κ-generalized statistics, is derived that is particularly suitable for describing the whole spectrum of incomes, from the low-middle income region up to the high income Pareto power-law regime. Analytical expressions for the shape, moments and some other basic statistical properties are given. Furthermore, several well-known econometric tools for measuring inequality, which all exist in a closed form, are considered. A method for parameter estimation is also discussed. The model is shown to fit remarkably well the data on personal income for the United States, and the analysis of inequality performed in terms of its parameters is revealed as very powerful.

A κ-generalized statistical mechanics approach to income analysis

International Nuclear Information System (INIS)

Clementi, F; Gallegati, M; Kaniadakis, G

2009-01-01

This paper proposes a statistical mechanics approach to the analysis of income distribution and inequality. A new distribution function, having its roots in the framework of κ-generalized statistics, is derived that is particularly suitable for describing the whole spectrum of incomes, from the low–middle income region up to the high income Pareto power-law regime. Analytical expressions for the shape, moments and some other basic statistical properties are given. Furthermore, several well-known econometric tools for measuring inequality, which all exist in a closed form, are considered. A method for parameter estimation is also discussed. The model is shown to fit remarkably well the data on personal income for the United States, and the analysis of inequality performed in terms of its parameters is revealed as very powerful

Alternative derivations of the statistical mechanical distribution laws.

Science.gov (United States)

Wall, F T

1971-08-01

A new approach is presented for the derivation of statistical mechanical distribution laws. The derivations are accomplished by minimizing the Helmholtz free energy under constant temperature and volume, instead of maximizing the entropy under constant energy and volume. An alternative method involves stipulating equality of chemical potential, or equality of activity, for particles in different energy levels. This approach leads to a general statement of distribution laws applicable to all systems for which thermodynamic probabilities can be written. The methods also avoid use of the calculus of variations, Lagrangian multipliers, and Stirling's approximation for the factorial. The results are applied specifically to Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. The special significance of chemical potential and activity is discussed for microscopic systems.

Algebraic methods in statistical mechanics and quantum field theory

CERN Document Server

Emch, Dr Gérard G

2009-01-01

This systematic algebraic approach concerns problems involving a large number of degrees of freedom. It extends the traditional formalism of quantum mechanics, and it eliminates conceptual and mathematical difficulties common to the development of statistical mechanics and quantum field theory. Further, the approach is linked to research in applied and pure mathematics, offering a reflection of the interplay between formulation of physical motivations and self-contained descriptions of the mathematical methods.The four-part treatment begins with a survey of algebraic approaches to certain phys

Geometry and topology in hamiltonian dynamics and statistical mechanics

CERN Document Server

Pettini, Marco

2007-01-01

Explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. This book provides an overview of the research in the area. Using geometrical thinking to solve fundamental problems in these areas could be highly productive

Multiple-shock initiation via statistical crack mechanics

Energy Technology Data Exchange (ETDEWEB)

Dienes, J.K.; Kershner, J.D.

1998-12-31

Statistical Crack Mechanics (SCRAM) is a theoretical approach to the behavior of brittle materials that accounts for the behavior of an ensemble of microcracks, including their opening, shear, growth, and coalescence. Mechanical parameters are based on measured strain-softening behavior. In applications to explosive and propellant sensitivity it is assumed that closed cracks act as hot spots, and that the heating due to interfacial friction initiates reactions which are modeled as one-dimensional heat flow with an Arrhenius source term, and computed in a subscale grid. Post-ignition behavior of hot spots is treated with the burn model of Ward, Son and Brewster. Numerical calculations using SCRAM-HYDROX are compared with the multiple-shock experiments of Mulford et al. in which the particle velocity in PBX 9501 is measured with embedded wires, and reactions are initiated and quenched.

An analysis of Greek seismicity based on Non Extensive Statistical Physics: The interdependence of magnitude, interevent time and interevent distance.

Science.gov (United States)

Efstathiou, Angeliki; Tzanis, Andreas; Vallianatos, Filippos

2014-05-01

aftershocks are the link between the main shocks and their remote offshoot. Overall, the above results compare well to the results of North Californian seismicity which have shown that the expression of seismicity at Northern California is generally consistent with non-extensive (sub-extensive) thermodynamics. Acknowledgments: This work was supported by the THALES Program of the Ministry of Education of Greece and the European Union in the framework of the project "Integrated understanding of Seismicity, using innovative methodologies of Fracture Mechanics along with Earthquake and Non-Extensive Statistical Physics - Application to the geodynamic system of the Hellenic Arc - SEISMO FEAR HELLARC". References: Tzanis A., Vallianatos F., Efstathiou A., Multidimensional earthquake frequency distributions consistent with Non-Extensive Statistical Physics: the interdependence of magnitude, interevent time and interevent distance in North California. Bulletin of the Geological Society of Greece, vol. XLVII 2013. Proceedings of the 13th International Congress, Chania, Sept. 2013 Tzanis A., Vallianatos F., Efstathiou A., Generalized multidimensional earthquake frequency distributions consistent with Non-Extensive Statistical Physics: An appraisal of the universality in the interdependence of magnitude, interevent time and interevent distance Geophysical Research Abstracts, Vol. 15, EGU2013-628, 2013, EGU General Assembly 2013 Marsan, D. and Lengliné, O., 2008. Extending earthquakes's reach through cascading, Science, 319, 1076; doi: 10.1126/science.1148783 On-line Bulletin, http://www.isc.ac.uk, Internatl. Seis. Cent., Thatcham, United Kingdom, 2011.

Statistical mechanics of budget-constrained auctions

International Nuclear Information System (INIS)

Altarelli, F; Braunstein, A; Realpe-Gomez, J; Zecchina, R

2009-01-01

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being in the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). On the basis of the cavity method of statistical mechanics, we introduce a message-passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise

Statistical mechanics of budget-constrained auctions

Science.gov (United States)

Altarelli, F.; Braunstein, A.; Realpe-Gomez, J.; Zecchina, R.

2009-07-01

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being in the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). On the basis of the cavity method of statistical mechanics, we introduce a message-passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.

Statistical mechanics of dense granular media

International Nuclear Information System (INIS)

Coniglio, A; Fierro, A; Nicodemi, M; Ciamarra, M Pica; Tarzia, M

2005-01-01

We discuss some recent results on the statistical mechanics approach to dense granular media. In particular, by analytical mean field investigation we derive the phase diagram of monodisperse and bidisperse granular assemblies. We show that 'jamming' corresponds to a phase transition from a 'fluid' to a 'glassy' phase, observed when crystallization is avoided. The nature of such a 'glassy' phase turns out to be the same as found in mean field models for glass formers. This gives quantitative evidence for the idea of a unified description of the 'jamming' transition in granular media and thermal systems, such as glasses. We also discuss mixing/segregation transitions in binary mixtures and their connections to phase separation and 'geometric' effects

SRB states and nonequilibrium statistical mechanics close to equilibrium

OpenAIRE

Gallavotti, Giovannni; Ruelle, David

1996-01-01

Nonequilibrium statistical mechanics close to equilibrium is studied using SRB states and a formula for their derivatives with respect to parameters. We write general expressions for the thermodynamic fluxes (or currents) and the transport coefficients, generalizing previous results. In this framework we give a general proof of the Onsager reciprocity relations.

Nonextensive Pythagoras' Theorem

OpenAIRE

Dukkipati, Ambedkar

2006-01-01

Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...

Thermodynamics and statistical mechanics an integrated approach

CERN Document Server

Hardy, Robert J

2014-01-01

This textbook brings together the fundamentals of the macroscopic and microscopic aspects of thermal physics by presenting thermodynamics and statistical mechanics as complementary theories based on small numbers of postulates. The book is designed to give the instructor flexibility in structuring courses for advanced undergraduates and/or beginning graduate students and is written on the principle that a good text should also be a good reference. The presentation of thermodynamics follows the logic of Clausius and Kelvin while relating the concepts involved to familiar phenomena and the mod

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

Statistical and stochastic aspects of the delocalization problem in quantum mechanics

International Nuclear Information System (INIS)

Claverie, P.; Diner, S.

1976-01-01

The space-time behaviour of electrons in atoms and molecules is reviewed. The wave conception of the electron is criticized and the poverty of the non-reductionist attitude is underlined. Further, the two main interpretations of quantum mechanics are recalled: the Copenhagen and the Statistical Interpretations. The meaning and the successes of the Statistical Interpretation are explained and it is shown that it does not solve all problems because quantum mechanics is irreducible to a classical statistical theory. The fluctuation of the particle number and its relationship to loge theory, delocalization and correlation is studied. Finally, different stochastic models for microphysics are reviewed. The markovian Fenyes-Nelson process allows an interpretation of the original heuristic considerations of Schroedinger. Non-markov processes with Schroedinger time evolution are shown to be equivalent to the base state analysis of Feynmann but they are unsatisfactory from a probabilistic point of view. Stochastic electrodynamics is presented as the most satisfactory conception nowadays

Statistical Mechanics Analysis of ATP Binding to a Multisubunit Enzyme

International Nuclear Information System (INIS)

Zhang Yun-Xin

2014-01-01

Due to inter-subunit communication, multisubunit enzymes usually hydrolyze ATP in a concerted fashion. However, so far the principle of this process remains poorly understood. In this study, from the viewpoint of statistical mechanics, a simple model is presented. In this model, we assume that the binding of ATP will change the potential of the corresponding enzyme subunit, and the degree of this change depends on the state of its adjacent subunits. The probability of enzyme in a given state satisfies the Boltzmann's distribution. Although it looks much simple, this model can fit the recent experimental data of chaperonin TRiC/CCT well. From this model, the dominant state of TRiC/CCT can be obtained. This study provide a new way to understand biophysical processe by statistical mechanics analysis. (interdisciplinary physics and related areas of science and technology)

Grassmann methods in lattice field theory and statistical mechanics

International Nuclear Information System (INIS)

Bilgici, E.; Gattringer, C.; Huber, P.

2006-01-01

Full text: In two dimensions models of loops can be represented as simple Grassmann integrals. In our work we explore the generalization of these techniques to lattice field theories and statistical mechanic systems in three and four dimensions. We discuss possible strategies and applications for representations of loop and surface models as Grassmann integrals. (author)

Derivation of some new distributions in statistical mechanics using maximum entropy approach

Directory of Open Access Journals (Sweden)

Ray Amritansu

2014-01-01

Full Text Available The maximum entropy principle has been earlier used to derive the Bose Einstein(B.E., Fermi Dirac(F.D. & Intermediate Statistics(I.S. distribution of statistical mechanics. The central idea of these distributions is to predict the distribution of the microstates, which are the particle of the system, on the basis of the knowledge of some macroscopic data. The latter information is specified in the form of some simple moment constraints. One distribution differs from the other in the way in which the constraints are specified. In the present paper, we have derived some new distributions similar to B.E., F.D. distributions of statistical mechanics by using maximum entropy principle. Some proofs of B.E. & F.D. distributions are shown, and at the end some new results are discussed.

Addressing the statistical mechanics of planet orbits in the solar system

Science.gov (United States)

Mogavero, Federico

2017-10-01

The chaotic nature of planet dynamics in the solar system suggests the relevance of a statistical approach to planetary orbits. In such a statistical description, the time-dependent position and velocity of the planets are replaced by the probability density function (PDF) of their orbital elements. It is natural to set up this kind of approach in the framework of statistical mechanics. In the present paper, I focus on the collisionless excitation of eccentricities and inclinations via gravitational interactions in a planetary system. The future planet trajectories in the solar system constitute the prototype of this kind of dynamics. I thus address the statistical mechanics of the solar system planet orbits and try to reproduce the PDFs numerically constructed by Laskar (2008, Icarus, 196, 1). I show that the microcanonical ensemble of the Laplace-Lagrange theory accurately reproduces the statistics of the giant planet orbits. To model the inner planets I then investigate the ansatz of equiprobability in the phase space constrained by the secular integrals of motion. The eccentricity and inclination PDFs of Earth and Venus are reproduced with no free parameters. Within the limitations of a stationary model, the predictions also show a reasonable agreement with Mars PDFs and that of Mercury inclination. The eccentricity of Mercury demands in contrast a deeper analysis. I finally revisit the random walk approach of Laskar to the time dependence of the inner planet PDFs. Such a statistical theory could be combined with direct numerical simulations of planet trajectories in the context of planet formation, which is likely to be a chaotic process.

q-triplet for Brazos River discharge: The edge of chaos?

Science.gov (United States)

Stosic, Tatijana; Stosic, Borko; Singh, Vijay P.

2018-04-01

We study the daily discharge data of Brazos River in Texas, USA, from 1900 to 2017, in terms of concepts drawn from the non-extensive statistics recently introduced by Tsallis. We find that the Brazos River discharge indeed follows non-extensive statistics regarding equilibrium, relaxation and sensitivity. Besides being the first such finding of a full-fledged q-triplet in hydrological data with possible future impact on water resources management, the fact that all three Tsallis q-triplet values are remarkably close to those of the logistic map at the onset of chaos opens up new questions towards a deeper understanding of the Brazos River dynamics, that may prove relevant for hydrological research in a more general sense.

Time series analysis of diverse extreme phenomena: universal features

Science.gov (United States)

Eftaxias, K.; Balasis, G.

2012-04-01

The field of study of complex systems holds that the dynamics of complex systems are founded on universal principles that may used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. We suggest that earthquake, epileptic seizures, solar flares, and magnetic storms dynamics can be analyzed within similar mathematical frameworks. A central property of aforementioned extreme events generation is the occurrence of coherent large-scale collective behavior with very rich structure, resulting from repeated nonlinear interactions among the corresponding constituents. Consequently, we apply the Tsallis nonextensive statistical mechanics as it proves an appropriate framework in order to investigate universal principles of their generation. First, we examine the data in terms of Tsallis entropy aiming to discover common "pathological" symptoms of transition to a significant shock. By monitoring the temporal evolution of the degree of organization in time series we observe similar distinctive features revealing significant reduction of complexity during their emergence. Second, a model for earthquake dynamics coming from a nonextensive Tsallis formalism, starting from first principles, has been recently introduced. This approach leads to an energy distribution function (Gutenberg-Richter type law) for the magnitude distribution of earthquakes, providing an excellent fit to seismicities generated in various large geographic areas usually identified as seismic regions. We show that this function is able to describe the energy distribution (with similar non-extensive q-parameter) of solar flares, magnetic storms, epileptic and earthquake shocks. The above mentioned evidence of a universal statistical behavior suggests the possibility of a common approach for studying space weather, earthquakes and epileptic seizures.

Statistical mechanical perturbation theory of solid-vapor interfacial free energy

NARCIS (Netherlands)

Kalikmanov, Vitalij Iosifovitsj; Hagmeijer, Rob; Venner, Cornelis H.

2017-01-01

The solid–vapor interfacial free energy γsv plays an important role in a number of physical phenomena, such as adsorption, wetting, and adhesion. We propose a closed form expression for the orientation averaged value of this quantity using a statistical mechanical perturbation approach developed in

Statistical Mechanical Perturbation Theory of Solid−Vapor Interfacial Free Energy

NARCIS (Netherlands)

Kalikmanov, V.I.; Hagmeijer, R.; Venner, C.H.

2017-01-01

The solid–vapor interfacial free energy γsv plays an important role in a number of physical phenomena, such as adsorption, wetting, and adhesion. We propose a closed form expression for the orientation averaged value of this quantity using a statistical mechanical perturbation approach developed in

Introduction to conformal invariance in statistical mechanics and to random surface models

International Nuclear Information System (INIS)

David, F.

1995-01-01

In the first part of these lectures I give a brief and somewhat superficial introduction to the techniques of conformal invariance and to a few applications in statistical mechanics in two dimensions. My purpose is to introduce the basic ideas and some standard results for the students who are not familiar with the theory, and to introduce concepts and tools which will be useful for the other lecturers, rather than to give a complete and up to date review of the subject. In the second part I discuss several problems in the statistical mechanics of two dimensional random surfaces and membranes. As an introduction, I present some basic facts about the statistical mechanics of one-dimensional objects and polymers, which are classical examples of objects with critical properties. Then I emphasize the special role of curvature energy and of the elastic energy associated with the internal structure of membranes, and the corresponding models of random surfaces. Finally, I discuss the specific problem of self-avoiding tethered surfaces, whose critical properties are still poorly understood, and for which the applicability of some basic techniques of field theory, such as renormalization group calculations, has been understood only recently. (orig.)

Statistical mechanical analysis of LMFBR fuel cladding tubes

International Nuclear Information System (INIS)

Poncelet, J.-P.; Pay, A.

1977-01-01

The most important design requirement on fuel pin cladding for LMFBR's is its mechanical integrity. Disruptive factors include internal pressure from mixed oxide fuel fission gas release, thermal stresses and high temperature creep, neutron-induced differential void-swelling as a source of stress in the cladding and irradiation creep of stainless steel material, corrosion by fission products. Under irradiation these load-restraining mechanisms are accentuated by stainless steel embrittlement and strength alterations. To account for the numerous uncertainties involved in the analysis by theoretical models and computer codes statistical tools are unavoidably requested, i.e. Monte Carlo simulation methods. Thanks to these techniques, uncertainties in nominal characteristics, material properties and environmental conditions can be linked up in a correct way and used for a more accurate conceptual design. (Auth.)

Statistical-mechanical lattice models for protein-DNA binding in chromatin

International Nuclear Information System (INIS)

Teif, Vladimir B; Rippe, Karsten

2010-01-01

Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibria measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical-mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.

Text mining by Tsallis entropy

Science.gov (United States)

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.

On a representation of the inverse Fq-transform

International Nuclear Information System (INIS)

Umarov, Sabir; Tsallis, Constantino

2008-01-01

A generalization of the Central Limit Theorem consistent with nonextensive statistical mechanics has been recently achieved through a generalized Fourier transform, noted q-Fourier transform. A representation formula for the inverse q-Fourier transform is here obtained in the class of functions G=U 1≤q G q , where G q ={f=ae q -βx 2 ,a>0,β>0}. This constitutes a first step towards a general representation of the inverse q-Fourier operation, which would enable interesting physical and other applications

Statistical mechanics of lattice Boson field theory

International Nuclear Information System (INIS)

1976-01-01

A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3 and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region

Statistical mechanics of lattice boson field theory

International Nuclear Information System (INIS)

Baker, G.A. Jr.

1977-01-01

A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3, and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region. 24 references

Bayesian Statistical Mechanics: Entropy-Enthalpy Compensation and Universal Equation of State at the Tip of Pen

Directory of Open Access Journals (Sweden)

Evgeni B. Starikov

2018-02-01

Full Text Available This work has shown the way to put the formal statistical-mechanical basement under the hotly debated notion of enthalpy-entropy compensation. The possibility of writing down the universal equation of state based upon the statistical mechanics is discussed here.

On the statistical mechanics of species abundance distributions.

Science.gov (United States)

Bowler, Michael G; Kelly, Colleen K

2012-09-01

A central issue in ecology is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to species abundance distributions (SADs) shows that simple ecological properties could account for the near universal features observed. These properties are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates. They underpin the neutral theory of Hubbell (2001), the master equation approach of Volkov et al. (2003, 2005) and the idiosyncratic (extreme niche) theory of Pueyo et al. (2007); they result in an underlying log series SAD, regardless of neutral or niche dynamics. The success of statistical mechanics in this application implies that communities are in dynamic equilibrium and hence that niches must be flexible and that temporal fluctuations on all sorts of scales are likely to be important in community structure. Copyright © 2012 Elsevier Inc. All rights reserved.

Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.

Science.gov (United States)

Gogolin, Christian; Eisert, Jens

2016-05-01

We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.

Statistical mechanics in the context of special relativity. II.

Science.gov (United States)

Kaniadakis, G

2005-09-01

The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various physical observables (e.g., momentum, energy, etc.), as well as the mathematical apparatus of the theory. Here, following the general lines of [Phys. Rev. E 66, 056125 (2002)], we show that the Lorentz transformations impose also a proper one-parameter generalization of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits us to construct a coherent and self-consistent relativistic statistical theory, preserving the main features of the ordinary statistical theory, which is recovered in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence. Furthermore, this statistical mechanics can be obtained as the stationary case of a generalized kinetic theory governed by an evolution equation obeying the H theorem and reproducing the Boltzmann equation of the ordinary kinetics in the classical limit.

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.

Science.gov (United States)

Sinitskiy, Anton V; Voth, Gregory A

2015-09-07

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

International Nuclear Information System (INIS)

Sinitskiy, Anton V.; Voth, Gregory A.

2015-01-01

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments

Dark matter and gas density profiles - a consequence of entropy bifurcation

International Nuclear Information System (INIS)

Leubner, M. P.

2006-01-01

The radial profiles of dark matter and hot plasma density distributions of relaxed galaxies and clusters were hitherto commonly fitted by empirical functions. On the other hand, the fundamental concept of non-extensive statistics accounts for long-range interactions and correlations present in gravitationally coupled ensembles and plasmas. We provide a theoretical link of non-extensive statistics to large scale astrophysical structures and show that the underlying tandem character of the entropy results in a bifurcation of the density distribution. A kinetic dark matter and thermodynamic gas branch turn out as natural consequence within the theory and is controlled by one single parameter, measuring physically the degree of correlations in the system. The theoretically derived density profiles are shown to represent accurately the characteristics of both, DM and hot plasma distributions, as observed or generated in N-body and hydro-simulations. The significant advantage over empirical fitting functions is provided by the physical content of the non-extensive approach wherefore it is proposed to model observed density profiles of astrophysical structures within the fundamental context of entropy generalization, accounting for nonlocality and long-range interactions in gravitationally coupled systems

Ergodic theory, interpretations of probability and the foundations of statistical mechanics

NARCIS (Netherlands)

van Lith, J.H.

2001-01-01

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time

Statistical methods in the mechanical design of fuel assemblies

Energy Technology Data Exchange (ETDEWEB)

Radsak, C.; Streit, D.; Muench, C.J. [AREVA NP GmbH, Erlangen (Germany)

2013-07-01

The mechanical design of a fuel assembly is still being mainly performed in a de terministic way. This conservative approach is however not suitable to provide a realistic quantification of the design margins with respect to licensing criter ia for more and more demanding operating conditions (power upgrades, burnup increase,..). This quantification can be provided by statistical methods utilizing all available information (e.g. from manufacturing, experience feedback etc.) of the topic under consideration. During optimization e.g. of the holddown system certain objectives in the mechanical design of a fuel assembly (FA) can contradict each other, such as sufficient holddown forces enough to prevent fuel assembly lift-off and reducing the holddown forces to minimize axial loads on the fuel assembly structure to ensure no negative effect on the control rod movement.By u sing a statistical method the fuel assembly design can be optimized much better with respect to these objectives than it would be possible based on a deterministic approach. This leads to a more realistic assessment and safer way of operating fuel assemblies. Statistical models are defined on the one hand by the quanti le that has to be maintained concerning the design limit requirements (e.g. one FA quantile) and on the other hand by the confidence level which has to be met. Using the above example of the holddown force, a feasible quantile can be define d based on the requirement that less than one fuel assembly (quantile > 192/19 3 [%] = 99.5 %) in the core violates the holddown force limit w ith a confidence of 95%. (orig.)

A Note on Burg’s Modified Entropy in Statistical Mechanics

Directory of Open Access Journals (Sweden)

Amritansu Ray

2016-02-01

Full Text Available Burg’s entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg’s Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg’s modified entropy is a better measure than the standard Burg’s entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg’s modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg’s modified entropy is used instead of conventional Burg’s entropy in a maximum entropy probability density (MEPD function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.

Statistical mechanics of learning orthogonal signals for general covariance models

International Nuclear Information System (INIS)

Hoyle, David C

2010-01-01

Statistical mechanics techniques have proved to be useful tools in quantifying the accuracy with which signal vectors are extracted from experimental data. However, analysis has previously been limited to specific model forms for the population covariance C, which may be inappropriate for real world data sets. In this paper we obtain new statistical mechanical results for a general population covariance matrix C. For data sets consisting of p sample points in R N we use the replica method to study the accuracy of orthogonal signal vectors estimated from the sample data. In the asymptotic limit of N,p→∞ at fixed α = p/N, we derive analytical results for the signal direction learning curves. In the asymptotic limit the learning curves follow a single universal form, each displaying a retarded learning transition. An explicit formula for the location of the retarded learning transition is obtained and we find marked variation in the location of the retarded learning transition dependent on the distribution of population covariance eigenvalues. The results of the replica analysis are confirmed against simulation

Statistical mechanics of driven diffusive systems

CERN Document Server

Schmittmann, B

1995-01-01

Far-from-equilibrium phenomena, while abundant in nature, are not nearly as well understood as their equilibrium counterparts. On the theoretical side, progress is slowed by the lack of a simple framework, such as the Boltzmann-Gbbs paradigm in the case of equilibrium thermodynamics. On the experimental side, the enormous structural complexity of real systems poses serious obstacles to comprehension. Similar difficulties have been overcome in equilibrium statistical mechanics by focusing on model systems. Even if they seem too simplistic for known physical systems, models give us considerable insight, provided they capture the essential physics. They serve as important theoretical testing grounds where the relationship between the generic physical behavior and the key ingredients of a successful theory can be identified and understood in detail. Within the vast realm of non-equilibrium physics, driven diffusive systems form a subset with particularly interesting properties. As a prototype model for these syst...

Statistical mechanical analysis of the linear vector channel in digital communication

International Nuclear Information System (INIS)

Takeda, Koujin; Hatabu, Atsushi; Kabashima, Yoshiyuki

2007-01-01

A statistical mechanical framework to analyze linear vector channel models in digital wireless communication is proposed for a large system. The framework is a generalization of that proposed for code-division multiple-access systems in Takeda et al (2006 Europhys. Lett. 76 1193) and enables the analysis of the system in which the elements of the channel transfer matrix are statistically correlated with each other. The significance of the proposed scheme is demonstrated by assessing the performance of an existing model of multi-input multi-output communication systems

To the problem of the statistical basis of evaluation of the mechanical safety factor

International Nuclear Information System (INIS)

Tsyganov, S.V.

2009-01-01

The methodology applied for the safety factor assessment of the WWER fuel cycles uses methods and terms of statistics. Value of the factor is calculated on the basis of estimation of probability to meet predefined limits. Such approach demands the special attention to the statistical properties of parameters of interest. Considering the mechanical constituents of the engineering factor it is assumed uncertainty factors of safety parameters are stochastic values. It characterized by probabilistic distributions that can be unknown. Traditionally in the safety factor assessment process the unknown parameters are estimated from the conservative points of view. This paper analyses how the refinement of the factors distribution parameters is important for the assessment of the mechanical safety factor. For the analysis the statistical approach is applied for modelling of different type of factor probabilistic distributions. It is shown the significant influence of the shape and parameters of distributions for some factors on the value of mechanical safety factor. (Authors)

To the problem of the statistical basis of evaluation of the mechanical safety factor

International Nuclear Information System (INIS)

Tsyganov, S.

2009-01-01

The methodology applied for the safety factor assessment of the VVER fuel cycles uses methods and terms of statistics. Value of the factor is calculated on the basis of estimation of probability to meet predefined limits. Such approach demands the special attention to the statistical properties of parameters of interest. Considering the mechanical constituents of the engineering factor it is assumed uncertainty factors of safety parameters are stochastic values. It characterized by probabilistic distributions that can be unknown. Traditionally in the safety factor assessment process the unknown parameters are estimated from the conservative points of view. This paper analyses how the refinement of the factors distribution parameters is important for the assessment of the mechanical safety factor. For the analysis the statistical approach is applied for modelling of different type of factor probabilistic distributions. It is shown the significant influence of the shape and parameters of distributions for some factors on the value of mechanical safety factor. (author)

BOOK REVIEW: Statistical Mechanics of Turbulent Flows

Science.gov (United States)

Cambon, C.

2004-10-01

This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their

Combining Generalized Renewal Processes with Non-Extensive Entropy-Based q-Distributions for Reliability Applications

Directory of Open Access Journals (Sweden)

Isis Didier Lins

2018-03-01

Full Text Available The Generalized Renewal Process (GRP is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribution, widely used in the reliability context. In this paper, we develop novel GRP models based on probability distributions that stem from the Tsallis’ non-extensive entropy, namely the q-Exponential and the q-Weibull distributions. The q-Exponential and Weibull distributions can model decreasing, constant or increasing failure intensity functions. However, the power law behavior of the q-Exponential probability density function for specific parameter values is an advantage over the Weibull distribution when adjusting data containing extreme values. The q-Weibull probability distribution, in turn, can also fit data with bathtub-shaped or unimodal failure intensities in addition to the behaviors already mentioned. Therefore, the q-Exponential-GRP is an alternative for the Weibull-GRP model and the q-Weibull-GRP generalizes both. The method of maximum likelihood is used for their parameters’ estimation by means of a particle swarm optimization algorithm, and Monte Carlo simulations are performed for the sake of validation. The proposed models and algorithms are applied to examples involving reliability-related data of complex systems and the obtained results suggest GRP plus q-distributions are promising techniques for the analyses of repairable systems.

Statistical mechanics, gravity, and Euclidean theory

International Nuclear Information System (INIS)

Fursaev, Dmitri V.

2002-01-01

A review of computations of free energy for Gibbs states on stationary but not static gravitational and gauge backgrounds is given. On these backgrounds wave equations for free fields are reduced to eigenvalue problems which depend non-linearly on the spectral parameter. We present a method to deal with such problems. In particular, we demonstrate how some results of the spectral theory of second-order elliptic operators, such as heat kernel asymptotics, can be extended to a class of non-linear spectral problems. The method is used to trace down the relation between the canonical definition of the free energy based on summation over the modes and the covariant definition given in Euclidean quantum gravity. As an application, high-temperature asymptotics of the free energy and of the thermal part of the stress-energy tensor in the presence of rotation are derived. We also discuss statistical mechanics in the presence of Killing horizons where canonical and Euclidean theories are related in a non-trivial way

Generalized bond percolation and statistical mechanics

International Nuclear Information System (INIS)

Tsallis, C.

1978-05-01

A generalization of traditional bond percolation is performed, in the sens that bonds have now the possibility of partially transmitting the information (a fact which leads to the concept of 'fidelity' of the bond), and also in the sens that, besides the normal tendency to equiprobability, the bonds are allowed to substantially change the information. Furthermore the fidelity is allowed, to become an aleatory variable, and the operational rules concerning the associated distribution laws are determined. Thermally quenched random bonds and the whole body of Statistical Mechanics become particular cases of this formalism, which is in general adapted to the treatment of all problems whose main characteristic is to preserve a part of the information through a long path or array (critical phenomena, regime changements, thermal random models, etc). Operationally it provides a quick method for the calculation of the equivalent probability of complex clusters within the traditional bond percolation problem [pt

Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions

NARCIS (Netherlands)

Marcolli, Matilde; Cornelissen, Gunther

2014-01-01

The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical (QSM) system, built from abelian class field theory. We introduce a general notion of isomorphism of QSM-systems and prove that it preserves (extremal) KMS equilibrium

PREFACE: Counting Complexity: An international workshop on statistical mechanics and combinatorics

Science.gov (United States)

de Gier, Jan; Warnaar, Ole

2006-07-01

On 10-15 July 2005 the conference `Counting Complexity: An international workshop on statistical mechanics and combinatorics' was held on Dunk Island, Queensland, Australia in celebration of Tony Guttmann's 60th birthday. Dunk Island provided the perfect setting for engaging in almost all of Tony's life-long passions: swimming, running, food, wine and, of course, plenty of mathematics and physics. The conference was attended by many of Tony's close scientific friends from all over the world, and most talks were presented by his past and present collaborators. This volume contains the proceedings of the meeting and consists of 24 refereed research papers in the fields of statistical mechanics, condensed matter physics and combinatorics. These papers provide an excellent illustration of the breadth and scope of Tony's work. The very first contribution, written by Stu Whittington, contains an overview of the many scientific achievements of Tony over the past 40 years in mathematics and physics. The organizing committee, consisting of Richard Brak, Aleks Owczarek, Jan de Gier, Emma Lockwood, Andrew Rechnitzer and Ole Warnaar, gratefully acknowledges the Australian Mathematical Society (AustMS), the Australian Mathematical Sciences Institute (AMSI), the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), the ARC Complex Open Systems Research Network (COSNet), the Institute of Physics (IOP) and the Department of Mathematics and Statistics of The University of Melbourne for financial support in organizing the conference. Tony, we hope that your future years in mathematics will be numerous. Count yourself lucky! Tony Guttman

The Big World of Nanothermodynamics

Directory of Open Access Journals (Sweden)

Ralph V. Chamberlin

2014-12-01

Full Text Available Nanothermodynamics extends standard thermodynamics to facilitate finite-size effects on the scale of nanometers. A key ingredient is Hill’s subdivision potential that accommodates the non-extensive energy of independent small systems, similar to how Gibbs’ chemical potential accommodates distinct particles. Nanothermodynamics is essential for characterizing the thermal equilibrium distribution of independently relaxing regions inside bulk samples, as is found for the primary response of most materials using various experimental techniques. The subdivision potential ensures strict adherence to the laws of thermodynamics: total energy is conserved by including an instantaneous contribution from the entropy of local configurations, and total entropy remains maximized by coupling to a thermal bath. A unique feature of nanothermodynamics is the completely-open nanocanonical ensemble. Another feature is that particles within each region become statistically indistinguishable, which avoids non-extensive entropy, and mimics quantum-mechanical behavior. Applied to mean-field theory, nanothermodynamics gives a heterogeneous distribution of regions that yields stretched-exponential relaxation and super-Arrhenius activation. Applied to Monte Carlo simulations, there is a nonlinear correction to Boltzmann’s factor that improves agreement between the Ising model and measured non-classical critical scaling in magnetic materials. Nanothermodynamics also provides a fundamental mechanism for the 1/f noise found in many materials.

From inverse problems to learning: a Statistical Mechanics approach

Science.gov (United States)

Baldassi, Carlo; Gerace, Federica; Saglietti, Luca; Zecchina, Riccardo

2018-01-01

We present a brief introduction to the statistical mechanics approaches for the study of inverse problems in data science. We then provide concrete new results on inferring couplings from sampled configurations in systems characterized by an extensive number of stable attractors in the low temperature regime. We also show how these result are connected to the problem of learning with realistic weak signals in computational neuroscience. Our techniques and algorithms rely on advanced mean-field methods developed in the context of disordered systems.

On the geometry of the spin-statistics connection in quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Reyes, A.

2006-07-01

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishability and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be

PREFACE: International Workshop on Statistical-Mechanical Informatics 2008 (IW-SMI 2008)

Science.gov (United States)

Hayashi, Masahito; Inoue, Jun-ichi; Kabashima, Yoshiyuki; Tanaka, Kazuyuki

2009-01-01

Statistical mechanical informatics (SMI) is an approach that applies physics to information science, in which many-body problems in information processing are tackled using statistical mechanics methods. In the last decade, the use of SMI has resulted in great advances in research into classical information processing, in particular, theories of information and communications, probabilistic inference and combinatorial optimization problems. It is expected that the success of SMI can be extended to quantum systems. The importance of many-body problems is also being recognized in quantum information theory (QIT), for which quantification of entanglement of bipartite systems has recently been almost completely established after considerable effort. SMI and QIT are sufficiently well developed that it is now appropriate to consider applying SMI to quantum systems and developing many-body theory in QIT. This combination of SMI and QIT is highly likely to contribute significantly to the development of both research fields. The International Workshop on Statistical-Mechanical Informatics has been organized in response to this situation. This workshop, held at Sendai International Conference Center, Sendai, Japan, 14-17 September 2008, and sponsored by the Grant-in-Aid for Scientific Research on Priority Areas `Deepening and Expansion of Statistical Mechanical Informatics (DEX-SMI)' (Head investigator: Yoshiyuki Kabashima, Tokyo Institute of Technology) (Project http://dex-smi.sp.dis.titech.ac.jp/DEX-SMI), was intended to provide leading researchers with strong interdisciplinary interests in QIT and SMI with the opportunity to engage in intensive discussions. The aim of the workshop was to expand SMI to quantum systems and QIT research on quantum (entangled) many-body systems, to discuss possible future directions, and to offer researchers the opportunity to exchange ideas that may lead to joint research initiatives. We would like to thank the contributors of the workshop

Statistical mechanics of directed models of polymers in the square lattice

International Nuclear Information System (INIS)

Rensburg, E J Janse van

2003-01-01

Directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature. These are idealized geometric directed lattice models introduced to study phase behaviour in polymers, and include Dyck paths, partially directed paths, directed trees and directed vesicles models. Directed models are closely related to models studied in the combinatorics literature (and are often exactly solvable). They are also simplified versions of a number of statistical mechanics models, including the self-avoiding walk, lattice animals and lattice vesicles. The exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models, and this will be explored in this review. The combinatorial nature of directed lattice path models makes a study using generating function approaches most natural. In contrast, the statistical mechanics approach would introduce partition functions and free energies, and then investigate these using the general framework of critical phenomena. Generating function and statistical mechanics approaches are closely related. For example, questions regarding the limiting free energy may be approached by considering the radius of convergence of a generating function, and the scaling properties of thermodynamic quantities are related to the asymptotic properties of the generating function. In this review the methods for obtaining generating functions and determining free energies in directed lattice path models of linear polymers is presented. These methods include decomposition methods leading to functional recursions, as well as the Temperley method (that is implemented by creating a combinatorial object, one slice at a time). A constant term formulation of the generating function will also be reviewed. The thermodynamic features and critical behaviour in models of directed paths may be

Current algebra, statistical mechanics and quantum models

Science.gov (United States)

Vilela Mendes, R.

2017-11-01

Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.

Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory

Science.gov (United States)

Ingber, Lester

1994-05-01

Previous papers in this series of statistical mechanics of neocortical interactions (SMNI) have detailed a development from the relatively microscopic scales of neurons up to the macroscopic scales as recorded by electroencephalography (EEG), requiring an intermediate mesocolumnar scale to be developed at the scale of minicolumns (~=102 neurons) and macrocolumns (~=105 neurons). Opportunity was taken to view SMNI as sets of statistical constraints, not necessarily describing specific synaptic or neuronal mechanisms, on neuronal interactions, on some aspects of short-term memory (STM), e.g., its capacity, stability, and duration. A recently developed c-language code, pathint, provides a non-Monte Carlo technique for calculating the dynamic evolution of arbitrary-dimension (subject to computer resources) nonlinear Lagrangians, such as derived for the two-variable SMNI problem. Here, pathint is used to explicitly detail the evolution of the SMNI constraints on STM.

Statistical mechanics of dense plasmas and implications for the plasma polarization shift

International Nuclear Information System (INIS)

Rogers, F.J.

1984-01-01

A brief description of the statistical mechanics of reacting, dense, plasmas is given. The results do not support a Debye-like polarization shift at low density. It is shown that the electronic charge density factors into a strongly quantum mechanical part, that is not much affected by many body correlations and a weakly quantum mechanical part, that is considerably effected by many body correlations. The few body charge density is obtained from direct solution of the Schroedinger equation and the many body charge density is obtained from the hypernetted chain equation through the introduction of a pseudopotential

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

Science.gov (United States)

Takabe, Satoshi; Hukushima, Koji

2016-05-01

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems.

Science.gov (United States)

Takabe, Satoshi; Hukushima, Koji

2016-05-01

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.

Statistical mechanics of relativistic spin-1 bosons in a magnetic field

International Nuclear Information System (INIS)

Daicic, J.; Frankel, N.E.

1993-01-01

This paper investigates the statistical mechanics of a gas of spin-1 particles with pair creation in a homogeneous magnetic field. It is shown that expansions for the thermodynamic potential and magnetization in fields below the mass scale of the constituent particles are well behaved. However, when the field is at or above the mass scale, an intrinsic pathology of the single-particle energy spectrum manifests itself in the statistical mechanics of the system. Whilst for the spin-0 and spin-1/2 analog of this system there seemed to be no barrier ab initio to the field strength, the nature of the vacuum, and the role of interactions, were always borne in mind as matters to be considered in a high-order treatment, particularly when the field was at or above the mass scale. In the spin-1 case, the pathology in the single-particle energy spectrum heralds this from the beginning, and seems to be a warning that a single particle non-interacting picture of physics at high energies needs some reconsideration. 10 refs

An introduction to conformal invariance in quantum field theory and statistical mechanics

International Nuclear Information System (INIS)

Boyanovsky, D.; Naon, C.M.

1990-01-01

The subject of conformal invariance provides an extraordinarly successful and productive symbiosis between statistical mechanics and quantum field theory. The main goal of this paper, which is tailored to a wide audience, is to give an introduction to such vast subject (C.P.)

Statistical mechanics of magnetized pair Fermi gas

International Nuclear Information System (INIS)

Daicic, J.; Frankel, N.E.; Kowalenko, V.

1993-01-01

Following previous work on the magnetized pair Bose gas this contribution presents the statistical mechanics of the charged relativistic Fermi gas with pair creation in d spatial dimensions. Initially, the gas in no external fields is studied. As a result, expansions for the various thermodynamic functions are obtained in both the μ/m→0 (neutrino) limit, and about the point μ/m =1, where μ is the chemical potential. The thermodynamics of a gas of quantum-number conserving massless fermions is also discussed. Then a complete study of the pair Fermi gas in a homogeneous magnetic field, is presented investigating the behavior of the magnetization over a wide range of field strengths. The inclusion of pairs leads to new results for the net magnetization due to the paramagnetic moment of the spins and the diamagnetic Landau orbits. 20 refs

Two statistical mechanics aspects of complex networks

Science.gov (United States)

Thurner, Stefan; Biely, Christoly

2006-12-01

By adopting an ensemble interpretation of non-growing rewiring networks, network theory can be reduced to a counting problem of possible network states and an identification of their associated probabilities. We present two scenarios of how different rewirement schemes can be used to control the state probabilities of the system. In particular, we review how by generalizing the linking rules of random graphs, in combination with superstatistics and quantum mechanical concepts, one can establish an exact relation between the degree distribution of any given network and the nodes’ linking probability distributions. In a second approach, we control state probabilities by a network Hamiltonian, whose characteristics are motivated by biological and socio-economical statistical systems. We demonstrate that a thermodynamics of networks becomes a fully consistent concept, allowing to study e.g. ‘phase transitions’ and computing entropies through thermodynamic relations.

Statistical learning: a powerful mechanism that operates by mere exposure.

Science.gov (United States)

Aslin, Richard N

2017-01-01

How do infants learn so rapidly and with little apparent effort? In 1996, Saffran, Aslin, and Newport reported that 8-month-old human infants could learn the underlying temporal structure of a stream of speech syllables after only 2 min of passive listening. This demonstration of what was called statistical learning, involving no instruction, reinforcement, or feedback, led to dozens of confirmations of this powerful mechanism of implicit learning in a variety of modalities, domains, and species. These findings reveal that infants are not nearly as dependent on explicit forms of instruction as we might have assumed from studies of learning in which children or adults are taught facts such as math or problem solving skills. Instead, at least in some domains, infants soak up the information around them by mere exposure. Learning and development in these domains thus appear to occur automatically and with little active involvement by an instructor (parent or teacher). The details of this statistical learning mechanism are discussed, including how exposure to specific types of information can, under some circumstances, generalize to never-before-observed information, thereby enabling transfer of learning. WIREs Cogn Sci 2017, 8:e1373. doi: 10.1002/wcs.1373 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

Solvability of a class of systems of infinite-dimensional integral equations and their application in statistical mechanics

International Nuclear Information System (INIS)

Gonchar, N.S.

1986-01-01

This paper presents a mathematical method developed for investigating a class of systems of infinite-dimensional integral equations which have application in statistical mechanics. Necessary and sufficient conditions are obtained for the uniqueness and bifurcation of the solution of this class of systems of equations. Problems of equilibrium statistical mechanics are considered on the basis of this method

From statistic mechanic outside equilibrium to transport equations

International Nuclear Information System (INIS)

Balian, R.

1995-01-01

This lecture notes give a synthetic view on the foundations of non-equilibrium statistical mechanics. The purpose is to establish the transport equations satisfied by the relevant variables, starting from the microscopic dynamics. The Liouville representation is introduced, and a projection associates with any density operator , for given choice of relevant observables, a reduced density operator. An exact integral-differential equation for the relevant variables is thereby derived. A short-memory approximation then yields the transport equations. A relevant entropy which characterizes the coarseness of the description is associated with each level of description. As an illustration, the classical gas, with its three levels of description and with the Chapman-Enskog method, is discussed. (author). 3 figs., 5 refs

The steady state of heterogeneous catalysis, studied by first-principles statistical mechanics

NARCIS (Netherlands)

Reuter, K.; Frenkel, D.; Scheffler, M.

2004-01-01

The turnover frequency of the catalytic oxidation of CO at RuO2(110) was calculated as a function of temperature and partial pressures using ab initio statistical mechanics. The underlying energetics of the gas-phase molecules, dissociation, adsorption, surface diffusion, surface chemical reactions,

Thermodynamics and statistical mechanics an integrated approach

CERN Document Server

Shell, M Scott

2015-01-01

Learn classical thermodynamics alongside statistical mechanics with this fresh approach to the subjects. Molecular and macroscopic principles are explained in an integrated, side-by-side manner to give students a deep, intuitive understanding of thermodynamics and equip them to tackle future research topics that focus on the nanoscale. Entropy is introduced from the get-go, providing a clear explanation of how the classical laws connect to the molecular principles, and closing the gap between the atomic world and thermodynamics. Notation is streamlined throughout, with a focus on general concepts and simple models, for building basic physical intuition and gaining confidence in problem analysis and model development. Well over 400 guided end-of-chapter problems are included, addressing conceptual, fundamental, and applied skill sets. Numerous worked examples are also provided together with handy shaded boxes to emphasize key concepts, making this the complete teaching package for students in chemical engineer...

Nonequilibrium phase transitions and bifurcations of limit cycles and tori- a new research topic for statistical mechanics mechanics

International Nuclear Information System (INIS)

Haken, H.

1980-01-01

In the development of statistical mechanics we can more or less distinguish between two steps. First of all the main objective of statistical mechanics had been to give thermodynamics a solid theoretical basis starting from the microscopic world. The next step has then been performed in parallel with the development of irreversible thermodynamics dealing with processes close to thermal equilibrium. The problems dealt with here are mainly transport and relaxation processes. Over the past years it has become apparent that there is a third field, namely processes far away from thermal equilibrium. The particular interest in those processes stems from the fact that in such situations order can be generated on a macroscopic scale. The ordered states can be maintained by a flux of energy or matter through, these systems. In the realm of synergetjcs we have studied numerous examples and we now know that the occurrence of many of the ordered structures is governed by the same basic principles. (author)

Nonequilibrium statistical mechanics and stochastic thermodynamics of small systems

International Nuclear Information System (INIS)

Tu Zhanchun

2014-01-01

Thermodynamics is an old subject. The research objects in conventional thermodynamics are macroscopic systems with huge number of particles. In recent 30 years, thermodynamics of small systems is a frontier topic in physics. Here we introduce nonequilibrium statistical mechanics and stochastic thermodynamics of small systems. As a case study, we construct a Canot-like cycle of a stochastic heat engine with a single particle controlled by a time-dependent harmonic potential. We find that the efficiency at maximum power is 1 - √T c /T h , where Tc and Th are the temperatures of cold bath and hot bath, respectively. (author)

Statistical mechanics of socio-economic systems with heterogeneous agents

International Nuclear Information System (INIS)

De Martino, Andrea; Marsili, Matteo

2006-01-01

We review the statistical mechanics approach to the study of the emerging collective behaviour of systems of heterogeneous interacting agents. The general framework is presented through examples in such contexts as ecosystem dynamics and traffic modelling. We then focus on the analysis of the optimal properties of large random resource-allocation problems and on Minority Games and related models of speculative trading in financial markets, discussing a number of extensions including multi-asset models, majority games and models with asymmetric information. Finally, we summarize the main conclusions and outline the major open problems and limitations of the approach. (topical review)

Statistics, synergy, and mechanism of multiple photogeneration of excitons in quantum dots: Fundamental and applied aspects

International Nuclear Information System (INIS)

Oksengendler, B. L.; Turaeva, N. N.; Uralov, I.; Marasulov, M. B.

2012-01-01

The effect of multiple exciton generation is analyzed based on statistical physics, quantum mechanics, and synergetics. Statistical problems of the effect of multiple exciton generation (MEG) are broadened and take into account not only exciton generation, but also background excitation. The study of the role of surface states of quantum dots is based on the synergy of self-catalyzed electronic reactions. An analysis of the MEG mechanism is based on the idea of electronic shaking using the sudden perturbation method in quantum mechanics. All of the above-mentioned results are applied to the problem of calculating the limiting efficiency to transform solar energy into electric energy. (authors)

Statistical fluid mechanics

CERN Document Server

Monin, A S

2007-01-01

""If ever a field needed a definitive book, it is the study of turbulence; if ever a book on turbulence could be called definitive, it is this book."" - ScienceWritten by two of Russia's most eminent and productive scientists in turbulence, oceanography, and atmospheric physics, this two-volume survey is renowned for its clarity as well as its comprehensive treatment. The first volume begins with an outline of laminar and turbulent flow. The remainder of the book treats a variety of aspects of turbulence: its statistical and Lagrangian descriptions, shear flows near surfaces and free turbulenc

Dimensionally regularized Tsallis' statistical mechanics and two-body Newton's gravitation

Science.gov (United States)

Zamora, J. D.; Rocca, M. C.; Plastino, A.; Ferri, G. L.

2018-05-01

Typical Tsallis' statistical mechanics' quantifiers like the partition function and the mean energy exhibit poles. We are speaking of the partition function Z and the mean energy 〈 U 〉 . The poles appear for distinctive values of Tsallis' characteristic real parameter q, at a numerable set of rational numbers of the q-line. These poles are dealt with dimensional regularization resources. The physical effects of these poles on the specific heats are studied here for the two-body classical gravitation potential.

Evaluation of mechanical properties of steel wire ropes by statistical methods

Directory of Open Access Journals (Sweden)

Boroška Ján

1999-12-01

Full Text Available The contribution deals with the evaluation of mechanical properties of steel wire ropes using statistical methods from the viewpoint of the quality of single wires as well as the internal construction of the wire ropes. The evaluation is based on the loading capacity calculated from the strength, number of folds and torsions. For the better ilustration, a box plot has been constructed.

Generalized quantum statistics

International Nuclear Information System (INIS)

Chou, C.

1992-01-01

In the paper, a non-anyonic generalization of quantum statistics is presented, in which Fermi-Dirac statistics (FDS) and Bose-Einstein statistics (BES) appear as two special cases. The new quantum statistics, which is characterized by the dimension of its single particle Fock space, contains three consistent parts, namely the generalized bilinear quantization, the generalized quantum mechanical description and the corresponding statistical mechanics

The Brandeis Dice Problem and Statistical Mechanics

Science.gov (United States)

van Enk, Steven J.

2014-11-01

Jaynes invented the Brandeis Dice Problem as a simple illustration of the MaxEnt (Maximum Entropy) procedure that he had demonstrated to work so well in Statistical Mechanics. I construct here two alternative solutions to his toy problem. One, like Jaynes' solution, uses MaxEnt and yields an analog of the canonical ensemble, but at a different level of description. The other uses Bayesian updating and yields an analog of the micro-canonical ensemble. Both, unlike Jaynes' solution, yield error bars, whose operational merits I discuss. These two alternative solutions are not equivalent for the original Brandeis Dice Problem, but become so in what must, therefore, count as the analog of the thermodynamic limit, M-sided dice with M → ∞. Whereas the mathematical analogies between the dice problem and Stat Mech are quite close, there are physical properties that the former lacks but that are crucial to the workings of the latter. Stat Mech is more than just MaxEnt.

8th Liblice Conference on the Statistical Mechanics of Liquids - Brno, Czech Republic, 13-18 June 2010 FOREWORD

Czech Academy of Sciences Publication Activity Database

Jackson, G.; Nezbeda, Ivo

2011-01-01

Roč. 190, 1 Sp.I:Sl (2011), s. 1-2 ISSN 0026-8976. [Liblice Conference on the Statistical Mechanics of Liquids /8./. Brno, 13.06.2010-18.06.2010] Institutional research plan: CEZ:AV0Z40720504 Keywords : editorial material * theories of liquids * statistical mechanics Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.819, year: 2011

Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography

Science.gov (United States)

Ingber, Lester

1991-09-01

A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions. While not useful to yield insights at the single-neuron level, SMNI has demonstrated its capability in describing large-scale properties of short-term memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numerical algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG and evoked-potential data being collected to investigate genetic predispositions to alcoholism and to extract brain ``signatures'' of short-term memory. Using the numerical algorithm of very fast simulated reannealing, it is demonstrated that SMNI can indeed fit these data within experimentally observed ranges of its underlying neuronal-synaptic parameters, and the quantitative modeling results are used to examine physical neocortical mechanisms to discriminate high-risk and low-risk populations genetically predisposed to alcoholism. Since this study is a control to span relatively long time epochs, similar to earlier attempts to establish such correlations, this discrimination is inconclusive because of other neuronal activity which can mask such effects. However, the SMNI model is shown to be consistent with EEG data during selective attention tasks and with neocortical mechanisms describing short-term memory previously published using this approach. This paper explicitly identifies similar nonlinear stochastic mechanisms of interaction at the microscopic-neuronal, mesoscopic-columnar, and macroscopic-regional scales of neocortical interactions. These results give strong quantitative support for an accurate intuitive picture, portraying

Statistical-Mechanical Analysis of Pre-training and Fine Tuning in Deep Learning

Science.gov (United States)

Ohzeki, Masayuki

2015-03-01

In this paper, we present a statistical-mechanical analysis of deep learning. We elucidate some of the essential components of deep learning — pre-training by unsupervised learning and fine tuning by supervised learning. We formulate the extraction of features from the training data as a margin criterion in a high-dimensional feature-vector space. The self-organized classifier is then supplied with small amounts of labelled data, as in deep learning. Although we employ a simple single-layer perceptron model, rather than directly analyzing a multi-layer neural network, we find a nontrivial phase transition that is dependent on the number of unlabelled data in the generalization error of the resultant classifier. In this sense, we evaluate the efficacy of the unsupervised learning component of deep learning. The analysis is performed by the replica method, which is a sophisticated tool in statistical mechanics. We validate our result in the manner of deep learning, using a simple iterative algorithm to learn the weight vector on the basis of belief propagation.

Metamodelling Messages Conveyed in Five Statistical Mechanical Textbooks from 1936 to 2001

Science.gov (United States)

Niss, Martin

2009-01-01

Modelling is a significant aspect of doing physics and it is important how this activity is taught. This paper focuses on the explicit or implicit messages about modelling conveyed to the student in the treatments of phase transitions in statistical mechanics textbooks at beginning graduate level. Five textbooks from the 1930s to the present are…

Escort entropies and divergences and related canonical distribution

International Nuclear Information System (INIS)

Bercher, J.-F.

2011-01-01

We discuss two families of two-parameter entropies and divergences, derived from the standard Renyi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions. Exploiting the nonnegativity of the divergences, we derive the expression of the canonical distribution associated to the new entropies and a observable given as an escort-mean value. We show that this canonical distribution extends, and smoothly connects, the results obtained in nonextensive thermodynamics for the standard and generalized mean value constraints. -- Highlights: → Two-parameter entropies are derived from q-entropies and escort distributions. → The related canonical distribution is derived. → This connects and extends known results in nonextensive statistics.

Statistical mechanics of fluids under internal constraints: Rigorous results for the one-dimensional hard rod fluid

International Nuclear Information System (INIS)

Corti, D.S.; Debenedetti, P.G.

1998-01-01

The rigorous statistical mechanics of metastability requires the imposition of internal constraints that prevent access to regions of phase space corresponding to inhomogeneous states. We derive exactly the Helmholtz energy and equation of state of the one-dimensional hard rod fluid under the influence of an internal constraint that places an upper bound on the distance between nearest-neighbor rods. This type of constraint is relevant to the suppression of boiling in a superheated liquid. We determine the effects of this constraint upon the thermophysical properties and internal structure of the hard rod fluid. By adding an infinitely weak and infinitely long-ranged attractive potential to the hard core, the fluid exhibits a first-order vapor-liquid transition. We determine exactly the equation of state of the one-dimensional superheated liquid and show that it exhibits metastable phase equilibrium. We also derive statistical mechanical relations for the equation of state of a fluid under the action of arbitrary constraints, and show the connection between the statistical mechanics of constrained and unconstrained ensembles. copyright 1998 The American Physical Society

Thermo-dynamical contours of electronic-vibrational spectra simulated using the statistical quantum-mechanical methods

DEFF Research Database (Denmark)

Pomogaev, Vladimir; Pomogaeva, Anna; Avramov, Pavel

2011-01-01

Three polycyclic organic molecules in various solvents focused on thermo-dynamical aspects were theoretically investigated using the recently developed statistical quantum mechanical/classical molecular dynamics method for simulating electronic-vibrational spectra. The absorption bands of estradiol...

Statistical mechanics of the interacting Yang-Mills instanton gas

International Nuclear Information System (INIS)

Ilgenfritz, E.-M.; Mueller-Preussker, M.

1980-01-01

Within the framework of the dilute gas approximation the instanton gas with dipole-like interaction is studied, including hard-core repulsion necessarily implied by the consistency of this approximation. A new, selfconsistent scheme is obtained of instanton calculations provided by a cooperative suppression of large instantons instead of the usual ad hoc infrared cut-off. Diluteness is better under control by a single, regularization prescription independent parameter. Functional methods known from statistical mechanics are used to treat the hard-core and dipole interactions simultaneously. The permeability of the instanton gas is calculated and used to discuss the Gell-Mann-Low β-function in the intermediate coupling range. The results are confronted with recent lattice calculations

A study of outliers in statistical distributions of mechanical properties of structural steels

International Nuclear Information System (INIS)

Oefverbeck, P.; Oestberg, G.

1977-01-01

The safety against failure of pressure vessels can be assessed by statistical methods, so-called probabilistic fracture mechanics. The data base for such estimations is admittedly rather meagre, making it necessary to assume certain conventional statistical distributions. Since the failure rates arrived at are low, for nuclear vessels of the order of 10 - to 10 - per year, the extremes of the variables involved, among other things the mechanical properties of the steel used, are of particular interest. A question sometimes raised is whether outliers, or values exceeding the extremes in the assumed distributions, might occur. In order to explore this possibility a study has been made of strength values of three qualities of structural steels, available in samples of up to about 12,000. Statistical evaluation of these samples with respect to outliers, using standard methods for this purpose, revealed the presence of such outliers in most cases, with a frequency of occurrence of, typically, a few values per thousand, estimated by the methods described. Obviously, statistical analysis alone cannot be expected to shed any light on the causes of outliers. Thus, the interpretation of these results with respect to their implication for the probabilistic estimation of the integrety of pressure vessels must await further studies of a similar nature in which the test specimens corresponding to outliers can be recovered and examined metallographically. For the moment the results should be regarded only as a factor to be considered in discussions of the safety of pressure vessels. (author)

Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

International Nuclear Information System (INIS)

Ichinose, Shoichi

2010-01-01

A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean coordinate system (X i ,τ) as the quantum statistical system of N quantum (statistical) variables (X τ ) and one Euclidean time variable (t). Introducing paths (lines or hypersurfaces) in this space (X τ ,t), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the mechanical system. The system Hamiltonian appears as the area. We show quantization is realized by the minimal area principle in the present geometric approach. When we take a line as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a hyper-surface as the path, the system Hamiltonian is given by the area of the hyper-surface which is defined as a closed-string configuration in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.

Fundamental problems in statistical mechanics VI. Proceedings of the sixth international summer school

Energy Technology Data Exchange (ETDEWEB)

Cohen, E G.D.

1985-01-01

The following topics were dealt with: walks, walls and ordering in low dimensions; renormalisation of fluids; wetting transition; phases and phase transitions; liquid-vapour interface; statistical mechanics in lattice gauge theory; hydrodynamic instabilities; complex dynamics and chaos; dynamical transitions; phase separation and pattern formation; kinetic theory of clustering; localisation.

Aftershock Energy Distribution by Statistical Mechanics Approach

Science.gov (United States)

Daminelli, R.; Marcellini, A.

2015-12-01

The aim of our work is to research the most probable distribution of the energy of aftershocks. We started by applying one of the fundamental principles of statistical mechanics that, in case of aftershock sequences, it could be expressed as: the greater the number of different ways in which the energy of aftershocks can be arranged among the energy cells in phase space the more probable the distribution. We assume that each cell in phase space has the same possibility to be occupied, and that more than one cell in the phase space can have the same energy. Seeing that seismic energy is proportional to products of different parameters, a number of different combinations of parameters can produce different energies (e.g., different combination of stress drop and fault area can release the same seismic energy). Let us assume that there are gi cells in the aftershock phase space characterised by the same energy released ɛi. Therefore we can assume that the Maxwell-Boltzmann statistics can be applied to aftershock sequences with the proviso that the judgment on the validity of this hypothesis is the agreement with the data. The aftershock energy distribution can therefore be written as follow: n(ɛ)=Ag(ɛ)exp(-βɛ)where n(ɛ) is the number of aftershocks with energy, ɛ, A and β are constants. Considering the above hypothesis, we can assume g(ɛ) is proportional to ɛ. We selected and analysed different aftershock sequences (data extracted from Earthquake Catalogs of SCEC, of INGV-CNT and other institutions) with a minimum magnitude retained ML=2 (in some cases ML=2.6) and a time window of 35 days. The results of our model are in agreement with the data, except in the very low energy band, where our model resulted in a moderate overestimation.

Statistical learning and probabilistic prediction in music cognition: mechanisms of stylistic enculturation.

Science.gov (United States)

Pearce, Marcus T

2018-05-11

Music perception depends on internal psychological models derived through exposure to a musical culture. It is hypothesized that this musical enculturation depends on two cognitive processes: (1) statistical learning, in which listeners acquire internal cognitive models of statistical regularities present in the music to which they are exposed; and (2) probabilistic prediction based on these learned models that enables listeners to organize and process their mental representations of music. To corroborate these hypotheses, I review research that uses a computational model of probabilistic prediction based on statistical learning (the information dynamics of music (IDyOM) model) to simulate data from empirical studies of human listeners. The results show that a broad range of psychological processes involved in music perception-expectation, emotion, memory, similarity, segmentation, and meter-can be understood in terms of a single, underlying process of probabilistic prediction using learned statistical models. Furthermore, IDyOM simulations of listeners from different musical cultures demonstrate that statistical learning can plausibly predict causal effects of differential cultural exposure to musical styles, providing a quantitative model of cultural distance. Understanding the neural basis of musical enculturation will benefit from close coordination between empirical neuroimaging and computational modeling of underlying mechanisms, as outlined here. © 2018 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals, Inc. on behalf of New York Academy of Sciences.

Multi-agent Negotiation Mechanisms for Statistical Target Classification in Wireless Multimedia Sensor Networks

Directory of Open Access Journals (Sweden)

Sheng Wang

2007-10-01

Full Text Available The recent availability of low cost and miniaturized hardware has allowedwireless sensor networks (WSNs to retrieve audio and video data in real worldapplications, which has fostered the development of wireless multimedia sensor networks(WMSNs. Resource constraints and challenging multimedia data volume makedevelopment of efficient algorithms to perform in-network processing of multimediacontents imperative. This paper proposes solving problems in the domain of WMSNs fromthe perspective of multi-agent systems. The multi-agent framework enables flexible networkconfiguration and efficient collaborative in-network processing. The focus is placed ontarget classification in WMSNs where audio information is retrieved by microphones. Todeal with the uncertainties related to audio information retrieval, the statistical approachesof power spectral density estimates, principal component analysis and Gaussian processclassification are employed. A multi-agent negotiation mechanism is specially developed toefficiently utilize limited resources and simultaneously enhance classification accuracy andreliability. The negotiation is composed of two phases, where an auction based approach isfirst exploited to allocate the classification task among the agents and then individual agentdecisions are combined by the committee decision mechanism. Simulation experiments withreal world data are conducted and the results show that the proposed statistical approachesand negotiation mechanism not only reduce memory and computation requi

A statistical mechanical model of economics

Science.gov (United States)

Lubbers, Nicholas Edward Williams

Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth vi condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex

On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data

Directory of Open Access Journals (Sweden)

Hans J. Haubold

2013-09-01

Full Text Available An entropy for the scalar variable case, parallel to Havrda-Charvat entropy, was introduced by the first author, and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined by the authors in previous papers. In the current paper, we extend the entropy to cover the scalar case, multivariable case, and matrix variate case. Then, this measure is optimized under different types of restrictions, and a number of models in the multivariable case and matrix variable case are obtained. Connections of these models to problems in statistical and physical sciences are pointed out. An application of the simplest case of the pathway model to the interpretation of solar neutrino data by applying standard deviation analysis and diffusion entropy analysis is provided.

Statistical mechanics of attractor neural network models with synaptic depression

International Nuclear Information System (INIS)

Igarashi, Yasuhiko; Oizumi, Masafumi; Otsubo, Yosuke; Nagata, Kenji; Okada, Masato

2009-01-01

Synaptic depression is known to control gain for presynaptic inputs. Since cortical neurons receive thousands of presynaptic inputs, and their outputs are fed into thousands of other neurons, the synaptic depression should influence macroscopic properties of neural networks. We employ simple neural network models to explore the macroscopic effects of synaptic depression. Systems with the synaptic depression cannot be analyzed due to asymmetry of connections with the conventional equilibrium statistical-mechanical approach. Thus, we first propose a microscopic dynamical mean field theory. Next, we derive macroscopic steady state equations and discuss the stabilities of steady states for various types of neural network models.

Statistical evaluation of the mechanical properties of high-volume class F fly ash concretes

KAUST Repository

Yoon, Seyoon; Monteiro, Paulo J.M.; Macphee, Donald E.; Glasser, Fredrik P.; Imbabi, Mohammed Salah-Eldin

2014-01-01

the authors experimentally and statistically investigated the effects of mix-design factors on the mechanical properties of high-volume class F fly ash concretes. A total of 240 and 32 samples were produced and tested in the laboratory to measure compressive

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

International Nuclear Information System (INIS)

Guo, Ran; Du, Jiulin

2015-01-01

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

Energy Technology Data Exchange (ETDEWEB)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.

Statistical mechanics view of quantum chromodynamics: Lattice gauge theory

International Nuclear Information System (INIS)

Kogut, J.B.

1984-01-01

Recent developments in lattice gauge theory are discussed from a statistial mechanics viewpoint. The basic physics problems of quantum chromodynamics (QCD) are reviewed for an audience of critical phenomena theorists. The idea of local gauge symmetry and color, the connection between statistical mechanics and field theory, asymptotic freedom and the continuum limit of lattice gauge theories, and the order parameters (confinement and chiral symmetry) of QCD are reviewed. Then recent developments in the field are discussed. These include the proof of confinement in the lattice theory, numerical evidence for confinement in the continuum limit of lattice gauge theory, and perturbative improvement programs for lattice actions. Next, we turn to the new challenges facing the subject. These include the need for a better understanding of the lattice Dirac equation and recent progress in the development of numerical methods for fermions (the pseudofermion stochastic algorithm and the microcanonical, molecular dynamics equation of motion approach). Finally, some of the applications of lattice gauge theory to QCD spectrum calculations and the thermodynamics of QCD will be discussed and a few remarks concerning future directions of the field will be made

A social discounting model based on Tsallis’ statistics

Science.gov (United States)

Takahashi, Taiki

2010-09-01

Social decision making (e.g. social discounting and social preferences) has been attracting attention in economics, econophysics, social physics, behavioral psychology, and neuroeconomics. This paper proposes a novel social discounting model based on the deformed algebra developed in the Tsallis’ non-extensive thermostatistics. Furthermore, it is suggested that this model can be utilized to quantify the degree of consistency in social discounting in humans and analyze the relationships between behavioral tendencies in social discounting and other-regarding economic decision making under game-theoretic conditions. Future directions in the application of the model to studies in econophysics, neuroeconomics, and social physics, as well as real-world problems such as the supply of live organ donations, are discussed.

A unified treatment of dynamics and scattering in classical and quantum statistical mechanics

International Nuclear Information System (INIS)

Prugovecki, E.

1978-01-01

The common formal features of classical and quantum statistical mechanics are investigated at three separate levels: at the level of L 2 spaces of wave-packets on GAMMA-space, of Liouville spaces B 2 consisting of density operators constructed from such wave-packets, and of phase-space representation spaces P of GAMMA distribution functions. It is shown that at the last level the formal similarities become so outstanding that all key quantities in P-space, such as Liouville operators, Hamiltonian functions, position and momentum observables, etc., are represented by expressions which to the zeroth order in (h/2π) coincide in the classical and quantum case, and in some instances coincide completely. Scattering theory on the B 2 Liouville spaces takes on the same formal appearance for classical and quantum statistical mechanics, and to the zeroth order in (h/2π) it coincides in both cases. This makes possible the formulation of a classical approximation to quantum scattering, and of a computational scheme for determining rhosup(out) from rhosup(in) for successive order of (h/2π). (Auth.)

Non extensive corrections to stellar nuclear reactions rate

Energy Technology Data Exchange (ETDEWEB)

Assuncao, M. [Universidade Federal de Sao Paulo (DCET/UNIFESP), Diadema, SP (Brazil). Dept. de Ciencias Exatas e da Terra; Silveira, F.E.M. [Universidade Federal do ABC, Santo Andre, SP (Brazil). Centro de Ciencias Naturais e Humanas; Lima, J.A.S. [Universidade de Sao Paulo (IAG/USP), SP (Brazil). Inst. de Astronomia, Geofisica e Ciencias Atmosfericas

2010-07-01

Full text: Stellar nucleosynthesis is widely accepted as the basic mechanism for creation of chemical elements in the Universe. In particular, nuclear reactions occurring in the Sun are recognized as responsible for its energy generation. The problem of to determine the energy generation mechanism in stars was firstly attacked by Gamow in the framework of his quantum mechanical theory of potential barrier penetration. According to that approach, the reactions rate is calculated by averaging the penetration factor over the velocity distribution of the plasma particles. A randomization of that distribution is expected as a consequence of the reactions. However, diffusion processes in the macroscopic environment should balance the resulting particles number depletion. Therefore, matter, energy, and momentum might steadily flow. In other words, a quasi-stationary equilibrium state must be attained. In this work, the potential barrier penetration approach to stellar nuclear reactions rate has been rediscussed with basis on Tsallis nonextensive statistics. The investigation has been restricted to non-resonant reactions, for which the S-factor can be regarded as a constant. It has been found that, within the extended formulation, the nonextensive q-parameter is constrained to a maximum value. Accordingly, the q-energy has been shown to exhibit a minimum. The q-Gamow peak has been derived and, in connection with the usual Gaussian approximation, the corresponding half q-width has been also estimated. Plots of the q-energy, q-Gamow peak and half q-width for some reactions with stellar physics interest have been produced. (author)

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

Science.gov (United States)

Pohorille, Andrew

2006-01-01

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described

Statistical mechanics of high-density bond percolation

Science.gov (United States)

Timonin, P. N.

2018-05-01

High-density (HD) percolation describes the percolation of specific κ -clusters, which are the compact sets of sites each connected to κ nearest filled sites at least. It takes place in the classical patterns of independently distributed sites or bonds in which the ordinary percolation transition also exists. Hence, the study of series of κ -type HD percolations amounts to the description of classical clusters' structure for which κ -clusters constitute κ -cores nested one into another. Such data are needed for description of a number of physical, biological, and information properties of complex systems on random lattices, graphs, and networks. They range from magnetic properties of semiconductor alloys to anomalies in supercooled water and clustering in biological and social networks. Here we present the statistical mechanics approach to study HD bond percolation on an arbitrary graph. It is shown that the generating function for κ -clusters' size distribution can be obtained from the partition function of the specific q -state Potts-Ising model in the q →1 limit. Using this approach we find exact κ -clusters' size distributions for the Bethe lattice and Erdos-Renyi graph. The application of the method to Euclidean lattices is also discussed.

Statistical mechanics approach to 1-bit compressed sensing

International Nuclear Information System (INIS)

Xu, Yingying; Kabashima, Yoshiyuki

2013-01-01

Compressed sensing is a framework that makes it possible to recover an N-dimensional sparse vector x∈R N from its linear transformation y∈R M of lower dimensionality M 1 -norm-based signal recovery scheme for 1-bit compressed sensing using statistical mechanics methods. We show that the signal recovery performance predicted by the replica method under the replica symmetric ansatz, which turns out to be locally unstable for modes breaking the replica symmetry, is in good consistency with experimental results of an approximate recovery algorithm developed earlier. This suggests that the l 1 -based recovery problem typically has many local optima of a similar recovery accuracy, which can be achieved by the approximate algorithm. We also develop another approximate recovery algorithm inspired by the cavity method. Numerical experiments show that when the density of nonzero entries in the original signal is relatively large the new algorithm offers better performance than the abovementioned scheme and does so with a lower computational cost. (paper)

Multi-agent Negotiation Mechanisms for Statistical Target Classification in Wireless Multimedia Sensor Networks

Science.gov (United States)

Wang, Xue; Bi, Dao-wei; Ding, Liang; Wang, Sheng

2007-01-01

The recent availability of low cost and miniaturized hardware has allowed wireless sensor networks (WSNs) to retrieve audio and video data in real world applications, which has fostered the development of wireless multimedia sensor networks (WMSNs). Resource constraints and challenging multimedia data volume make development of efficient algorithms to perform in-network processing of multimedia contents imperative. This paper proposes solving problems in the domain of WMSNs from the perspective of multi-agent systems. The multi-agent framework enables flexible network configuration and efficient collaborative in-network processing. The focus is placed on target classification in WMSNs where audio information is retrieved by microphones. To deal with the uncertainties related to audio information retrieval, the statistical approaches of power spectral density estimates, principal component analysis and Gaussian process classification are employed. A multi-agent negotiation mechanism is specially developed to efficiently utilize limited resources and simultaneously enhance classification accuracy and reliability. The negotiation is composed of two phases, where an auction based approach is first exploited to allocate the classification task among the agents and then individual agent decisions are combined by the committee decision mechanism. Simulation experiments with real world data are conducted and the results show that the proposed statistical approaches and negotiation mechanism not only reduce memory and computation requirements in WMSNs but also significantly enhance classification accuracy and reliability. PMID:28903223

A statistical mechanics model for free-for-all airplane passenger boarding

Science.gov (United States)

Steffen, Jason H.

2008-12-01

I discuss a model for free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics, where each seat in the aircraft has an associated energy which reflects the preferences of travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with those that involve assigned seats. The model can be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results might provide a useful description of this boarding method. The model is a relatively unusual application of undergraduate level physics and describes a situation familiar to many students and faculty.

A statistical mechanics model for free-for-all airplane passenger boarding

International Nuclear Information System (INIS)

Steffen, Jason H.; Fermilab

2008-01-01

I discuss a model for free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics where each seat in the aircraft has an associated energy which reflects the preferences of travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with those that involve assigned seats. The model can be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results might provide a useful description of this boarding method. The model is a relatively unusual application of undergraduate level physics and describes a situation familiar to many students and faculty

A statistical mechanics model for free-for-all airplane passenger boarding

Energy Technology Data Exchange (ETDEWEB)

Steffen, Jason H.; /Fermilab

2008-08-01

I discuss a model for free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics where each seat in the aircraft has an associated energy which reflects the preferences of travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with those that involve assigned seats. The model can be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results might provide a useful description of this boarding method. The model is a relatively unusual application of undergraduate level physics and describes a situation familiar to many students and faculty.

Infinite-mode squeezed coherent states and non-equilibrium statistical mechanics (phase-space-picture approach)

International Nuclear Information System (INIS)

Yeh, L.

1992-01-01

The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite- mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena

Statistical mechanics of the fashion game on random networks

International Nuclear Information System (INIS)

Sun, YiFan

2016-01-01

A model of fashion on networks is studied. This model consists of two groups of agents that are located on a network and have opposite viewpoints towards being fashionable: behaving consistently with either the majority or the minority of adjacent agents. Checking whether the fashion game has a pure Nash equilibrium (pure NE) is a non-deterministic polynomial complete problem. Using replica-symmetric mean field theory, the largest proportion of satisfied agents and the region where at least one pure NE should exist are determined for several types of random networks. Furthermore, a quantitive analysis of the asynchronous best response dynamics yields the phase diagram of existence and detectability of pure NE in the fashion game on some random networks. (paper: classical statistical mechanics, equilibrium and non-equilibrium).

Statistical-mechanics analysis of Gaussian labeled-unlabeled classification problems

International Nuclear Information System (INIS)

Tanaka, Toshiyuki

2013-01-01

The labeled-unlabeled classification problem in semi-supervised learning is studied via statistical-mechanics approach. We analytically investigate performance of a learner with an equal-weight mixture of two symmetrically-located Gaussians, performing posterior mean estimation of the parameter vector on the basis of a dataset consisting of labeled and unlabeled data generated from the same probability model as that assumed by the learner. Under the assumption of replica symmetry, we have analytically obtained a set of saddle-point equations, which allows us to numerically evaluate performance of the learner. On the basis of the analytical result we have observed interesting phenomena, in particular the coexistence of good and bad solutions, which may happen when the number of unlabeled data is relatively large compared with that of labeled data

A quantum information approach to statistical mechanics

International Nuclear Information System (INIS)

Cuevas, G.

2011-01-01

The field of quantum information and computation harnesses and exploits the properties of quantum mechanics to perform tasks more efficiently than their classical counterparts, or that may uniquely be possible in the quantum world. Its findings and techniques have been applied to a number of fields, such as the study of entanglement in strongly correlated systems, new simulation techniques for many-body physics or, generally, to quantum optics. This thesis aims at broadening the scope of quantum information theory by applying it to problems in statistical mechanics. We focus on classical spin models, which are toy models used in a variety of systems, ranging from magnetism, neural networks, to quantum gravity. We tackle these models using quantum information tools from three different angles. First, we show how the partition function of a class of widely different classical spin models (models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. We prove this by first establishing a relation between partition functions and quantum states, and then transforming the corresponding quantum states to each other. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proof is based on a relation between partition functions and quantum circuits, which allows us to determine the quantum computational complexity of the partition function by studying the corresponding quantum circuit. Finally, we outline the possibility of applying quantum information concepts and tools to certain models of dis- crete quantum gravity. The latter provide a natural route to generalize our results, insofar as the central quantity has the form of a partition function, and as classical spin models are used as toy models of matter. (author)

Plasma Soliton Turbulence and Statistical Mechanics

International Nuclear Information System (INIS)

Treumann, R.A.; Pottelette, R.

1999-01-01

Collisionless kinetic plasma turbulence is described approximately in terms of a superposition of non-interacting solitary waves. We discuss the relevance of such a description under astrophysical conditions. Several types of solitary waves may be of interest in this relation as generators of turbulence and turbulent transport. A consistent theory of turbulence can be given only in a few particular cases when the description can be reduced to the Korteweg-de Vries equation or some other simple equation like the Kadomtsev-Petviashvili equation. It turns out that the soliton turbulence is usually energetically harder than the ordinary weakly turbulent plasma description. This implies that interaction of particles with such kinds of turbulence can lead to stronger acceleration than in ordinary turbulence. However, the description in our model is only classical and non-relativistic. Transport in solitary turbulence is most important for drift wave turbulence. Such waves form solitary drift wave vortices which may provide cross-field transport. A more general discussion is given on transport. In a model of Levy flight trapping of particles in solitons (or solitary turbulence) one finds that the residence time of particles in the region of turbulence may be described by a generalized Lorentzian probability distribution. It is shown that under collisionless equilibrium conditions far away from thermal equilibrium such distributions are natural equilibrium distributions. A consistent thermodynamic description of such media can be given in terms of a generalized Lorentzian statistical mechanics and thermodynamics. (author)

Statistical mechanical foundation of the peridynamic nonlocal continuum theory: energy and momentum conservation laws.

Science.gov (United States)

Lehoucq, R B; Sears, Mark P

2011-09-01

The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.

Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow

Science.gov (United States)

Farrell, Brian F.; Ioannou, Petros J.

2017-08-01

This paper describes a study of the self-sustaining process in wall turbulence. The study is based on a second order statistical state dynamics model of Couette flow in which the state variables are the streamwise mean flow (first cumulant) and perturbation covariance (second cumulant). This statistical state dynamics model is closed by either setting the third cumulant to zero or by replacing it with a stochastic parametrization. Statistical state dynamics models with this form are referred to as S3T models. S3T models have been shown to self-sustain turbulence with a mean flow and second order perturbation structure similar to that obtained by direct numerical simulation of the equations of motion. The use of a statistical state dynamics model to study the physical mechanisms underlying turbulence has important advantages over the traditional approach of studying the dynamics of individual realizations of turbulence. One advantage is that the analytical structure of S3T statistical state dynamics models isolates the interaction between the mean flow and the perturbation components of the turbulence. Isolation of the interaction between these components reveals how this interaction underlies both the maintenance of the turbulence variance by transfer of energy from the externally driven flow to the perturbation components as well as the enforcement of the observed statistical mean turbulent state by feedback regulation between the mean and perturbation fields. Another advantage of studying turbulence using statistical state dynamics models of S3T form is that the analytical structure of S3T turbulence can be completely characterized. For example, the perturbation component of turbulence in the S3T system is demonstrably maintained by a parametric perturbation growth mechanism in which fluctuation of the mean flow maintains the perturbation field which in turn maintains the mean flow fluctuations in a synergistic interaction. Furthermore, the equilibrium

Statistical mechanics of gravitons in a box and the black hole entropy

Science.gov (United States)

Viaggiu, Stefano

2017-05-01

This paper is devoted to the study of the statistical mechanics of trapped gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a consequence, a discrete spectrum dependent on the Legendre index ℓ similar to the harmonic oscillator one is obtained and a statistical study is performed. The mean energy 〈 E 〉 results as a sum of two discrete Planck distributions with different dependent frequencies. As an important application, we derive the semiclassical Bekenstein-Hawking entropy formula for a static Schwarzschild black hole by only requiring that the black hole internal energy U is provided by its ADM rest energy, without invoking particular quantum gravity theories. This seriously suggests that the interior of a black hole can be composed of trapped gravitons at a thermodynamical temperature proportional by a factor ≃ 2 to the horizon temperature Th.

The Statistical Mechanics of Ideal MHD Turbulence

Science.gov (United States)

Shebalin, John V.

2003-01-01

Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.

Probabilistic cellular automata: Some statistical mechanical considerations

International Nuclear Information System (INIS)

Lebowitz, J.L.; Maes, C.; Speer, E.R.

1990-01-01

Spin systems evolving in continuous or discrete time under the action of stochastic dynamics are used to model phenomena as diverse as the structure of alloys and the functioning of neural networks. While in some cases the dynamics are secondary, designed to produce a specific stationary measure whose properties one is interested in studying, there are other cases in which the only available information is the dynamical rule. Prime examples of the former are computer simulations, via Glauber dynamics, of equilibrium Gibbs measures with a specified interaction potential. Examples of the latter include various types of majority rule dynamics used as models for pattern recognition and for error-tolerant computations. The present note discusses ways in which techniques found useful in equilibrium statistical mechanics can be applied to a particular class of models of the latter types. These are cellular automata with noise: systems in which the spins are updated stochastically at integer times, simultaneously at all sites of some regular lattice. These models were first investigated in detail in the Soviet literature of the late sixties and early seventies. They are now generally referred to as Stochastic or Probabilistic Cellular Automata (PCA), and may be considered to include deterministic automata (CA) as special limits. 16 refs., 3 figs

Statistics with JMP graphs, descriptive statistics and probability

CERN Document Server

Goos, Peter

2015-01-01

Peter Goos, Department of Statistics, University ofLeuven, Faculty of Bio-Science Engineering and University ofAntwerp, Faculty of Applied Economics, BelgiumDavid Meintrup, Department of Mathematics and Statistics,University of Applied Sciences Ingolstadt, Faculty of MechanicalEngineering, GermanyThorough presentation of introductory statistics and probabilitytheory, with numerous examples and applications using JMPDescriptive Statistics and Probability provides anaccessible and thorough overview of the most important descriptivestatistics for nominal, ordinal and quantitative data withpartic

An Overview of Generalized Gamma Mittag–Leffler Model and Its Applications

Directory of Open Access Journals (Sweden)

Seema S. Nair

2015-08-01

Full Text Available Recently, probability models with thicker or thinner tails have gained more importance among statisticians and physicists because of their vast applications in random walks, Lévi flights, financial modeling, etc. In this connection, we introduce here a new family of generalized probability distributions associated with the Mittag–Leffler function. This family gives an extension to the generalized gamma family, opens up a vast area of potential applications and establishes connections to the topics of fractional calculus, nonextensive statistical mechanics, Tsallis statistics, superstatistics, the Mittag–Leffler stochastic process, the Lévi process and time series. Apart from examining the properties, the matrix-variate analogue and the connection to fractional calculus are also explained. By using the pathway model of Mathai, the model is further generalized. Connections to Mittag–Leffler distributions and corresponding autoregressive processes are also discussed.

Statistical mechanics of Fermi-Pasta-Ulam chains with the canonical ensemble

Science.gov (United States)

Demirel, Melik C.; Sayar, Mehmet; Atılgan, Ali R.

1997-03-01

Low-energy vibrations of a Fermi-Pasta-Ulam-Β (FPU-Β) chain with 16 repeat units are analyzed with the aid of numerical experiments and the statistical mechanics equations of the canonical ensemble. Constant temperature numerical integrations are performed by employing the cubic coupling scheme of Kusnezov et al. [Ann. Phys. 204, 155 (1990)]. Very good agreement is obtained between numerical results and theoretical predictions for the probability distributions of the generalized coordinates and momenta both of the chain and of the thermal bath. It is also shown that the average energy of the chain scales linearly with the bath temperature.

Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity

Science.gov (United States)

Ingber, Lester

1984-06-01

A theory developed by the author to describe macroscopic neocortical interactions demonstrates that empirical values of chemical and electrical parameters of synaptic interactions establish several minima of the path-integral Lagrangian as a function of excitatory and inhibitory columnar firings. The number of possible minima, their time scales of hysteresis and probable reverberations, and their nearest-neighbor columnar interactions are all consistent with well-established empirical rules of human short-term memory. Thus, aspects of conscious experience are derived from neuronal firing patterns, using modern methods of nonlinear nonequilibrium statistical mechanics to develop realistic explicit synaptic interactions.

Functional differential equations for the q-Fourier transform of q-Gaussians

International Nuclear Information System (INIS)

Umarov, S; Queiros, S M Duarte

2010-01-01

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 ≤ q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Evidence for criticality in financial data

Science.gov (United States)

Ruiz, G.; de Marcos, A. F.

2018-01-01

We provide evidence that cumulative distributions of absolute normalized returns for the 100 American companies with the highest market capitalization, uncover a critical behavior for different time scales Δt. Such cumulative distributions, in accordance with a variety of complex - and financial - systems, can be modeled by the cumulative distribution functions of q-Gaussians, the distribution function that, in the context of nonextensive statistical mechanics, maximizes a non-Boltzmannian entropy. These q-Gaussians are characterized by two parameters, namely ( q, β), that are uniquely defined by Δt. From these dependencies, we find a monotonic relationship between q and β, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality.

National Astronomical Observatory of Japan

CERN Document Server

Haubold, Hans J; UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science, hosted by the National Astronomical Observatory of Japan

2010-01-01

This book represents Volume II of the Proceedings of the UN/ESA/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science, hosted by the National Astronomical Observatory of Japan, Tokyo, 18 - 22 June, 2007. It covers two programme topics explored in this and past workshops of this nature: (i) non-extensive statistical mechanics as applicable to astrophysics, addressing q-distribution, fractional reaction and diffusion, and the reaction coefficient, as well as the Mittag-Leffler function and (ii) the TRIPOD concept, developed for astronomical telescope facilities. The companion publication, Volume I of the proceedings of this workshop, is a special issue in the journal Earth, Moon, and Planets, Volume 104, Numbers 1-4, April 2009.

Functional differential equations for the q-Fourier transform of q-Gaussians

Energy Technology Data Exchange (ETDEWEB)

Umarov, S [Department of Mathematics, Tufts University, Medford, MA (United States); Queiros, S M Duarte, E-mail: sdqueiro@gmail.co [Unilever R and D Port Sunlight, Quarry Road East, Wirral, CH63 3JW (United Kingdom)

2010-02-05

In this paper the question 'is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor?' is studied for the whole range of q in (- infty, 3). This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. Using the functional differential equation approach we prove that the answer is affirmative if and only if 1 <= q < 3, excluding two particular cases of q < 1, namely q=1/2 and q=2/3. Complementarily, we discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.

Completely X-symmetric S-matrices corresponding to theta functions and models of statistical mechanics

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Chudnovsky, G.V.

1981-01-01

We consider general expressions of factorized S-matrices with Abelian symmetry expressed in terms of theta-functions. These expressions arise from representations of the Heisenberg group. New examples of factorized S-matrices lead to a large class of completely integrable models of statistical mechanics which generalize the XYZ-model of the eight-vertex model. (orig.)

Marginal instability threshold of magnetosonic waves in kappa distributed plasma

Science.gov (United States)

Bashir, M. F.; Manzoor, M. Z.; Ilie, R.; Yoon, P. H.; Miasli, M. S.

2017-12-01

The dispersion relation of magnetosonic wave is studied taking the non-extensive anisotropic counter-streaming distribution which follows the Tsallis statistics. The effects of non-extensivity parameter (q), counter-streaming parameter (P) and the wave-particle interaction is analyzed on the growth rate and the marginal instability threshold condition of Magnetosonic (MS) mode to provide the possible explanation of different regions the Bale-diagram obtained from the solar wind data at 1 AU as represented by the temperature anisotropy ( ) vs plasma beta ( ) solar wind data plot. It is shown that the most of the regions of Bale-diagram is bounded by the MS instability under different condition and best fitted by the non-extesnive distribution. The results for the bi-kappa distribution and bi- Maxwellian distribution are also obtained in the limits and respectively.

Statistical mechanics of lattice systems a concrete mathematical introduction

CERN Document Server

Friedli, Sacha

2017-01-01

This motivating textbook gives a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie–Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kać interactions. Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin–Wagner and Lee–Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov–Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make i...

Statistical mechanics of competitive resource allocation using agent-based models

Science.gov (United States)

Chakraborti, Anirban; Challet, Damien; Chatterjee, Arnab; Marsili, Matteo; Zhang, Yi-Cheng; Chakrabarti, Bikas K.

2015-01-01

Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game, Kolkata Paise Restaurant problem, Stable marriage problem, Parking space problem and others) and the methods used to understand them analytically. We emphasize the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder. As these methods can be applied to any large-scale model of competitive resource allocation made up of heterogeneous adaptive agent with non-linear interaction, they provide a prospective unifying paradigm for many scientific disciplines.

Infant Statistical Learning

Science.gov (United States)

Saffran, Jenny R.; Kirkham, Natasha Z.

2017-01-01

Perception involves making sense of a dynamic, multimodal environment. In the absence of mechanisms capable of exploiting the statistical patterns in the natural world, infants would face an insurmountable computational problem. Infant statistical learning mechanisms facilitate the detection of structure. These abilities allow the infant to compute across elements in their environmental input, extracting patterns for further processing and subsequent learning. In this selective review, we summarize findings that show that statistical learning is both a broad and flexible mechanism (supporting learning from different modalities across many different content areas) and input specific (shifting computations depending on the type of input and goal of learning). We suggest that statistical learning not only provides a framework for studying language development and object knowledge in constrained laboratory settings, but also allows researchers to tackle real-world problems, such as multilingualism, the role of ever-changing learning environments, and differential developmental trajectories. PMID:28793812

The non-equilibrium statistical mechanics of a simple geophysical fluid dynamics model

Science.gov (United States)

Verkley, Wim; Severijns, Camiel

2014-05-01

Lorenz [1] has devised a dynamical system that has proved to be very useful as a benchmark system in geophysical fluid dynamics. The system in its simplest form consists of a periodic array of variables that can be associated with an atmospheric field on a latitude circle. The system is driven by a constant forcing, is damped by linear friction and has a simple advection term that causes the model to behave chaotically if the forcing is large enough. Our aim is to predict the statistics of Lorenz' model on the basis of a given average value of its total energy - obtained from a numerical integration - and the assumption of statistical stationarity. Our method is the principle of maximum entropy [2] which in this case reads: the information entropy of the system's probability density function shall be maximal under the constraints of normalization, a given value of the average total energy and statistical stationarity. Statistical stationarity is incorporated approximately by using `stationarity constraints', i.e., by requiring that the average first and possibly higher-order time-derivatives of the energy are zero in the maximization of entropy. The analysis [3] reveals that, if the first stationarity constraint is used, the resulting probability density function rather accurately reproduces the statistics of the individual variables. If the second stationarity constraint is used as well, the correlations between the variables are also reproduced quite adequately. The method can be generalized straightforwardly and holds the promise of a viable non-equilibrium statistical mechanics of the forced-dissipative systems of geophysical fluid dynamics. [1] E.N. Lorenz, 1996: Predictability - A problem partly solved, in Proc. Seminar on Predictability (ECMWF, Reading, Berkshire, UK), Vol. 1, pp. 1-18. [2] E.T. Jaynes, 2003: Probability Theory - The Logic of Science (Cambridge University Press, Cambridge). [3] W.T.M. Verkley and C.A. Severijns, 2014: The maximum entropy

Existence and uniqueness of Gibbs states for a statistical mechanical polyacetylene model

International Nuclear Information System (INIS)

Park, Y.M.

1987-01-01

One-dimensional polyacetylene is studied as a model of statistical mechanics. In a semiclassical approximation the system is equivalent to a quantum XY model interacting with unbounded classical spins in one-dimensional lattice space Z. By establishing uniform estimates, an infinite-volume-limit Hilbert space, a strongly continuous time evolution group of unitary operators, and an invariant vector are constructed. Moreover, it is proven that any infinite-limit state satisfies Gibbs conditions. Finally, a modification of Araki's relative entropy method is used to establish the uniqueness of Gibbs states

Statistical mechanics of sparse generalization and graphical model selection

International Nuclear Information System (INIS)

Lage-Castellanos, Alejandro; Pagnani, Andrea; Weigt, Martin

2009-01-01

One of the crucial tasks in many inference problems is the extraction of an underlying sparse graphical model from a given number of high-dimensional measurements. In machine learning, this is frequently achieved using, as a penalty term, the L p norm of the model parameters, with p≤1 for efficient dilution. Here we propose a statistical mechanics analysis of the problem in the setting of perceptron memorization and generalization. Using a replica approach, we are able to evaluate the relative performance of naive dilution (obtained by learning without dilution, following by applying a threshold to the model parameters), L 1 dilution (which is frequently used in convex optimization) and L 0 dilution (which is optimal but computationally hard to implement). Whereas both L p diluted approaches clearly outperform the naive approach, we find a small region where L 0 works almost perfectly and strongly outperforms the simpler to implement L 1 dilution

Prehensile apparatus

Science.gov (United States)

Smith, C.M.

1993-10-12

The present invention relates to an apparatus for handling a workpiece comprising a vessel that is longitudinally extensible and pressurizable, and a nonextensible and laterally flexible member on the vessel. The member constrains one side of the vessel to be nonextensible, causing the vessel to bend in the direction of the nonextensible member when pressurized. 8 figures.

Statistical analysis of the factors that influenced the mechanical properties improvement of cassava starch films

Science.gov (United States)

Monteiro, Mayra; Oliveira, Victor; Santos, Francisco; Barros Neto, Eduardo; Silva, Karyn; Silva, Rayane; Henrique, João; Chibério, Abimaelle

2017-08-01

In order to obtain cassava starch films with improved mechanical properties in relation to the synthetic polymer in the packaging production, a complete factorial design 23 was carried out in order to investigate which factor significantly influences the tensile strength of the biofilm. The factors to be investigated were cassava starch, glycerol and modified clay contents. Modified bentonite clay was used as a filling material of the biofilm. Glycerol was the plasticizer used to thermoplastify cassava starch. The factorial analysis suggested a regression model capable of predicting the optimal mechanical property of the cassava starch film from the maximization of the tensile strength. The reliability of the regression model was tested by the correlation established with the experimental data through the following statistical analyse: Pareto graph. The modified clay was the factor of greater statistical significance on the observed response variable, being the factor that contributed most to the improvement of the mechanical property of the starch film. The factorial experiments showed that the interaction of glycerol with both modified clay and cassava starch was significant for the reduction of biofilm ductility. Modified clay and cassava starch contributed to the maximization of biofilm ductility, while glycerol contributed to the minimization.

The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved

International Nuclear Information System (INIS)

Samaj, L

2003-01-01

The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of this fluid model is exactly solvable via an equivalence with the integrable 2D sine-Gordon field theory. The exact solution includes the bulk thermodynamics, special cases of the surface thermodynamics and the large-distance asymptotic behaviour of the two-body correlation functions

Statistical Physics An Introduction

CERN Document Server

Yoshioka, Daijiro

2007-01-01

This book provides a comprehensive presentation of the basics of statistical physics. The first part explains the essence of statistical physics and how it provides a bridge between microscopic and macroscopic phenomena, allowing one to derive quantities such as entropy. Here the author avoids going into details such as Liouville’s theorem or the ergodic theorem, which are difficult for beginners and unnecessary for the actual application of the statistical mechanics. In the second part, statistical mechanics is applied to various systems which, although they look different, share the same mathematical structure. In this way readers can deepen their understanding of statistical physics. The book also features applications to quantum dynamics, thermodynamics, the Ising model and the statistical dynamics of free spins.

The statistical mechanics of financial markets

CERN Document Server

Voit, Johannes

2003-01-01

From the reviews of the first edition - "Provides an excellent introduction for physicists interested in the statistical properties of financial markets. Appropriately early in the book the basic financial terms such as shorts, limit orders, puts, calls, and other terms are clearly defined. Examples, often with graphs, augment the reader’s understanding of what may be a plethora of new terms and ideas… [This is] an excellent starting point for the physicist interested in the subject. Some of the book’s strongest features are its careful definitions, its detailed examples, and the connection it establishes to physical systems." PHYSICS TODAY "This book is excellent at illustrating the similarities of financial markets with other non-equilibrium physical systems. [...] In summary, a very good book that offers more than just qualitative comparisons of physics and finance." (www.quantnotes.com) This highly-praised introductory treatment describes parallels between statistical physics and finance - both thos...

Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Lauwers, P G

1990-12-01

Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: Stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. (orig.).

Statistical physics

CERN Document Server

Sadovskii, Michael V

2012-01-01

This volume provides a compact presentation of modern statistical physics at an advanced level. Beginning with questions on the foundations of statistical mechanics all important aspects of statistical physics are included, such as applications to ideal gases, the theory of quantum liquids and superconductivity and the modern theory of critical phenomena. Beyond that attention is given to new approaches, such as quantum field theory methods and non-equilibrium problems.

Neocortical dynamics at multiple scales: EEG standing waves, statistical mechanics, and physical analogs.

Science.gov (United States)

Ingber, Lester; Nunez, Paul L

2011-02-01

The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the importance of myelinated axon propagation delays and periodic boundary conditions in the cortical-white matter system, which is topologically close to a spherical shell. By contrast, the proposed local mechanisms are multiscale interactions between cortical columns via short-ranged non-myelinated fibers. A mechanical model consisting of a stretched string with attached nonlinear springs demonstrates the general idea. The string produces standing waves analogous to large-scale coherent EEG observed in some brain states. The attached springs are analogous to the smaller (mesoscopic) scale columnar dynamics. Generally, we expect string displacement and EEG at all scales to result from both global and local phenomena. A statistical mechanics of neocortical interactions (SMNI) calculates oscillatory behavior consistent with typical EEG, within columns, between neighboring columns via short-ranged non-myelinated fibers, across cortical regions via myelinated fibers, and also derives a string equation consistent with the global EEG model. Copyright © 2010 Elsevier Inc. All rights reserved.

Some properties of the representation of the quasilocal observables in statistical mechanics and quantum field theory

International Nuclear Information System (INIS)

Testard, D.; Centre National de la Recherche Scientifique, 13 - Marseille

1977-09-01

For a finite non zero temperature state in Statistical Mechanics it is proved that the factor obtained in the corresponding representation of the quasilocal algebra has the property of Araki. The same result also holds for the 'wedge-algebras' of a hermitian scalar Wightman field

Modulational instability: Conservation laws and bright soliton solution of ion-acoustic waves in electron-positron-ion-dust plasmas

Science.gov (United States)

EL-Kalaawy, O. H.

2018-02-01

We consider the nonlinear propagation of non-planar (cylindrical and spherical) ion-acoustic (IA) envelope solitary waves in an unmagnetized plasma consisting of electron-positron-ion-dust plasma with two-electron temperature distributions in the context of the non-extensive statistics. The basic set of fluid equations is reduced to the modified nonlinear Schrödinger (MNLS) equation in cylindrical and spherical geometry by using the reductive perturbation method (RPM). It is found that the nature of the modulational instabilities would be significantly modified due to the effects of the non-extensive and other plasma parameters as well as cylindrical and spherical geometry. Conservation laws of the MNLS equation are obtained by Lie symmetry and multiplier method. A new exact solution (envelope bright soliton) is obtained by the extended homogeneous balance method. Finally, we study the results of this article.

Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

Energy Technology Data Exchange (ETDEWEB)

Alamino, Roberto C; Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)

2007-10-12

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases.

Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

International Nuclear Information System (INIS)

Alamino, Roberto C; Saad, David

2007-01-01

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases

Reason of method of density functional in classical and quantum statistical mechanisms

International Nuclear Information System (INIS)

Dinariev, O.Yu.

2000-01-01

Interaction between phenomenological description of a multi-component mixture on the basis of entropy functional with members, square in terms of component density gradients and temperature, on the one hand, and description in the framework of classical and quantum statistical mechanics, on the other hand, was investigated. Explicit expressions for the entropy functional in the classical and quantum theory were derived. Then a square approximation for the case of minor disturbances of uniform state was calculated. In the approximation the addends square in reference to the gradient were singlet out. It permits calculation of the relevant phenomenological coefficients from the leading principles [ru

Statistical mechanics and dynamics of solvable models with long-range interactions

International Nuclear Information System (INIS)

Campa, Alessandro; Dauxois, Thierry; Ruffo, Stefano

2009-01-01

For systems with long-range interactions, the two-body potential decays at large distances as V(r)∼1/r α , with α≤d, where d is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics, two-dimensional elasticity, charged and dipolar systems. Although such systems can be made extensive, they are intrinsically non additive: the sum of the energies of macroscopic subsystems is not equal to the energy of the whole system. Moreover, the space of accessible macroscopic thermodynamic parameters might be non convex. The violation of these two basic properties of the thermodynamics of short-range systems is at the origin of ensemble inequivalence. In turn, this inequivalence implies that specific heat can be negative in the microcanonical ensemble, and temperature jumps can appear at microcanonical first order phase transitions. The lack of convexity allows us to easily spot regions of parameter space where ergodicity may be broken. Historically, negative specific heat had been found for gravitational systems and was thought to be a specific property of a system for which the existence of standard equilibrium statistical mechanics itself was doubted. Realizing that such properties may be present for a wider class of systems has renewed the interest in long-range interactions. Here, we present a comprehensive review of the recent advances on the statistical mechanics and out-of-equilibrium dynamics of solvable systems with long-range interactions. The core of the review consists in the detailed presentation of the concept of ensemble inequivalence, as exemplified by the exact solution, in the microcanonical and canonical ensembles, of mean-field type models. Remarkably, the entropy of all these models can be obtained using the method of large deviations. Long-range interacting systems display an extremely slow relaxation towards thermodynamic equilibrium and, what is more striking, the convergence towards quasi-stationary states. The

New entropic uncertainty relations and tests of PMD-SQS-optimal limits in pion-nucleus scattering

International Nuclear Information System (INIS)

Ion, D.B.; Ion, M.L.

2002-01-01

In this paper we define a new kind of quantum entropy, namely, the nonextensivity conjugated entropy S Jθ (p,q) bar.Then we prove the optimal nonextensivity conjugated entropic uncertainty relations (ONC-EUR) as well as optimal nonextensivity conjugated entropic uncertainty bands (ONC E UB). The results of the first experimental test of ONC-EUB in the pion-nucleus scattering, obtained by using 49-sets of experimental phase shift analysis, are presented. So, strong evidences for the saturation of the PMD-SQS-optimum limit are obtained with high accuracy (confidence level > 99%) for the nonextensivities: 1/2 ≤ p ≤ 2/3 and q = p/(2p-1). (authors)

Statistical physics as an approximate method of many-body quantum mechanics in the representation of occupation numbers

International Nuclear Information System (INIS)

Kushnirenko, A.N.

1989-01-01

An attempt was made to substantiate statistical physics from the viewpoint of many-body quantum mechanics in the representation of occupation numbers. This approach enabled to develop the variation method for solution of stationary and nonstationary nonequilibrium problems

Fractional statistics and quantum theory

CERN Document Server

Khare, Avinash

1997-01-01

This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f

Statistical evaluation of low cycle loading curves parameters for structural materials by mechanical characteristics

International Nuclear Information System (INIS)

Daunys, Mykolas; Sniuolis, Raimondas

2006-01-01

About 300 welded joint materials that are used in nuclear power energy were tested under monotonous tension and low cycle loading in Kaunas University of Technology together with St. Peterburg Central Research Institute of Structural Materials in 1970-2000. The main mechanical, low cycle loading and fracture characteristics of base metals, weld metals and some heat-affected zones of welded joints metals were determined during these experiments. Analytical dependences of low cycle fatigue parameters on mechanical characteristics of structural materials were proposed on the basis of a large number of experimental data, obtained by the same methods and testing equipment. When these dependences are used, expensive low cycle fatigue tests may be omitted and it is possible to compute low cycle loading curves parameters and lifetime for structural materials according to the main mechanical characteristics given in technical manuals. Dependences of low cycle loading curves parameters on mechanical characteristics for several groups of structural materials used in Russian nuclear power energy are obtained by statistical methods and proposed in this paper

Fundamental properties of fracture and seismicity in a non extensive statistical physics framework.

Science.gov (United States)

Vallianatos, Filippos

2010-05-01

classical normalization of p(X). The second one is based on the definition of the expectation value which has to be generalized to the "q-expectation value", according to the generalization of the entropy [Abe and Suzuki, 2003]. In order to calculate p(X) we apply the technique of Langrange multipliers maximizing an appropriate functional and leading tο maximization of the Tsallis entropy under the constraints on the normalization and the q-expectation value. It is well known that the Gutenberg-Richter (G-R) power law distribution has to be modified for large seismic moments because of energy conservation and geometrical reasons. Several models have been proposed, either in terms of a second power law with a larger b value beyond a crossover magnitude, or based on a magnidute cut-off using an exponential taper. In the present work we point out that the non extensivity viewpoint is applicable to seismic processes. In the frame of a non-extensive approach which is based on Tsallis entropy we construct a generalized expression of Gutenberg-Richter (GGR) law [Vallianatos, 2008]. The existence of lower or/and upper bound to magnitude is discussed and the conditions under which GGR lead to classical GR law are analysed. For the lowest earthquake size (i.e., energy level) the correlation between the different parts of elements involved in the evolution of an earthquake are short-ranged and GR can be deduced on the basis of the maximum entropy principle using BG statistics. As the size (i.e., energy) increases, long range correlation becomes much more important, implying the necessity of using Tsallis entropy as an appropriate generalization of BG entropy. The power law behaviour is derived as a special case, leading to b-values being functions of the non-extensivity parameter q. Furthermore a theoretical analysis of similarities presented in stress stimulated electric and acoustic emissions and earthquakes are discussed not only in the frame of GGR but taking into account a

Statistical Mechanics and Applications in Condensed Matter

Science.gov (United States)

Di Castro, Carlo; Raimondi, Roberto

2015-08-01

Preface; 1. Thermodynamics: a brief overview; 2. Kinetics; 3. From Boltzmann to Gibbs; 4. More ensembles; 5. The thermodynamic limit and its thermodynamic stability; 6. Density matrix and quantum statistical mechanics; 7. The quantum gases; 8. Mean-field theories and critical phenomena; 9. Second quantization and Hartree-Fock approximation; 10. Linear response and fluctuation-dissipation theorem in quantum systems: equilibrium and small deviations; 11. Brownian motion and transport in disordered systems; 12. Fermi liquids; 13. The Landau theory of the second order phase transitions; 14. The Landau-Wilson model for critical phenomena; 15. Superfluidity and superconductivity; 16. The scaling theory; 17. The renormalization group approach; 18. Thermal Green functions; 19. The microscopic foundations of Fermi liquids; 20. The Luttinger liquid; 21. Quantum interference effects in disordered electron systems; Appendix A. The central limit theorem; Appendix B. Some useful properties of the Euler Gamma function; Appendix C. Proof of the second theorem of Yang and Lee; Appendix D. The most probable distribution for the quantum gases; Appendix E. Fermi-Dirac and Bose-Einstein integrals; Appendix F. The Fermi gas in a uniform magnetic field: Landau diamagnetism; Appendix G. Ising and gas-lattice models; Appendix H. Sum over discrete Matsubara frequencies; Appendix I. Hydrodynamics of the two-fluid model of superfluidity; Appendix J. The Cooper problem in the theory of superconductivity; Appendix K. Superconductive fluctuations phenomena; Appendix L. Diagrammatic aspects of the exact solution of the Tomonaga Luttinger model; Appendix M. Details on the theory of the disordered Fermi liquid; References; Author index; Index.

Statistical Mechanics of Money, Income, and Wealth

Science.gov (United States)

Yakovenko, Victor

2006-03-01

In Ref. [1], we proposed an analogy between the exponential Boltzmann-Gibbs distribution of energy in physics and the equilibrium probability distribution of money in a closed economic system. Analogously to energy, money is locally conserved in interactions between economic agents, so the thermal Boltzmann-Gibbs distribution function is expected for money. Since then, many researchers followed and expanded this idea [2]. Much work was done on the analysis of empirical data, mostly on income, for which a lot of tax and census data is available. We demonstrated [3] that income distribution in the USA has a well-defined two-class structure. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs (``thermal'') distribution. The upper class (1-3% of population) has a Pareto power-law (``superthermal'') distribution, whose parameters change in time with the rise and fall of stock market. We proposed a concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively demonstrated that it applies to the majority of population. Income distribution in other countries shows similar patterns. For more references, see http://www2.physics.umd.edu/˜yakovenk/econophysics.html. References: [1] A. A. Dragulescu and V. M. Yakovenko, ``Statistical mechanics of money'', Eur. Phys. J. B 17, 723 (2000). [2] ``Econophysics of Wealth Distributions'', edited by A. Chatterjee, S. Yarlagadda, and B. K. Chakrabarti, Springer, 2005. [3] A. C. Silva and V. M. Yakovenko, ``Temporal evolution of the `thermal' and `superthermal' income classes in the USA during 1983-2001'', Europhys. Lett. 69, 304 (2005).

Quark matter revisited with non-extensive MIT bag model

Energy Technology Data Exchange (ETDEWEB)

Cardoso, Pedro H.G.; Nunes da Silva, Tiago; Menezes, Debora P. [Universidade Federal de Santa Catarina, Departamento de Fisica, CFM, Florianopolis (Brazil); Deppman, Airton [Instituto de Fisica da Universidade de Sao Paulo, Sao Paulo (Brazil)

2017-10-15

In this work we revisit the MIT bag model to describe quark matter within both the usual Fermi-Dirac and the Tsallis statistics. We verify the effects of the non-additivity of the latter by analysing two different pictures: the first order phase transition of the QCD phase diagram and stellar matter properties. While the QCD phase diagram is visually affected by the Tsallis statistics, the resulting effects on quark star macroscopic properties are barely noticed. (orig.)

Portfolio optimization problem with nonidentical variances of asset returns using statistical mechanical informatics

Science.gov (United States)

Shinzato, Takashi

2016-12-01

The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We defined two characteristic quantities of an optimal portfolio, namely, minimal investment risk and investment concentration, in order to solve the portfolio optimization problem and analytically determined their asymptotical behaviors using replica analysis. Numerical experiments were also performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.

Methods of statistical physics

CERN Document Server

Akhiezer, Aleksandr I

1981-01-01

Methods of Statistical Physics is an exposition of the tools of statistical mechanics, which evaluates the kinetic equations of classical and quantized systems. The book also analyzes the equations of macroscopic physics, such as the equations of hydrodynamics for normal and superfluid liquids and macroscopic electrodynamics. The text gives particular attention to the study of quantum systems. This study begins with a discussion of problems of quantum statistics with a detailed description of the basics of quantum mechanics along with the theory of measurement. An analysis of the asymptotic be

Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion.

Science.gov (United States)

Gautestad, Arild O

2012-09-07

Animals moving under the influence of spatio-temporal scaling and long-term memory generate a kind of space-use pattern that has proved difficult to model within a coherent theoretical framework. An extended kind of statistical mechanics is needed, accounting for both the effects of spatial memory and scale-free space use, and put into a context of ecological conditions. Simulations illustrating the distinction between scale-specific and scale-free locomotion are presented. The results show how observational scale (time lag between relocations of an individual) may critically influence the interpretation of the underlying process. In this respect, a novel protocol is proposed as a method to distinguish between some main movement classes. For example, the 'power law in disguise' paradox-from a composite Brownian motion consisting of a superposition of independent movement processes at different scales-may be resolved by shifting the focus from pattern analysis at one particular temporal resolution towards a more process-oriented approach involving several scales of observation. A more explicit consideration of system complexity within a statistical mechanical framework, supplementing the more traditional mechanistic modelling approach, is advocated.

The Sigmoid Transfer Function and the Gain-threshold Exponential Dependence for Neurons from Statistical Mechanics Treatment

Czech Academy of Sciences Publication Activity Database

Andrey, Ladislav; Erzan, R.

2002-01-01

Roč. 52, č. 12 (2002), s. 1349-1356 ISSN 0011-4626 R&D Projects: GA ČR GA305/02/1487 Institutional research plan: AV0Z1030915 Keywords : nonlinear gain curve * gain-threshold dependence * non-monotone transfer function * statistical mechanics Subject RIV: BA - General Mathematics Impact factor: 0.311, year: 2002

Statistical methods and materials characterisation

International Nuclear Information System (INIS)

Wallin, K.R.W.

2010-01-01

Statistics is a wide mathematical area, which covers a myriad of analysis and estimation options, some of which suit special cases better than others. A comprehensive coverage of the whole area of statistics would be an enormous effort and would also be outside the capabilities of this author. Therefore, this does not intend to be a textbook on statistical methods available for general data analysis and decision making. Instead it will highlight a certain special statistical case applicable to mechanical materials characterization. The methods presented here do not in any way rule out other statistical methods by which to analyze mechanical property material data. (orig.)

Granular statistical mechanics - Building on the legacy of Sir Sam Edwards

Science.gov (United States)

Blumenfeld, Raphael

When Sir Sam Edwards laid down the foundations for the statistical mechanics of jammed granular materials he opened a new field in soft condensed matter and many followed. In this presentation we review briefly the Edwards formalism and some of its less discussed consequences. We point out that the formalism is useful for other classes of systems - cellular and porous materials. A certain shortcoming of the original formalism is then discussed and a modification to overcome it is proposed. Finally, a derivation of an equation of state with the new formalism is presented; the equation of state is analogous to the PVT relation for thermal gases, relating the volume, the boundary stress and measures of the structural and stress fluctuations. NUDT, Changsha, China, Imperial College London, UK, Cambridge University, UK.

An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action

Science.gov (United States)

Barra, Adriano; Contucci, Pierluigi; Sandell, Rickard; Vernia, Cecilia

2014-02-01

How does immigrant integration in a country change with immigration density? Guided by a statistical mechanics perspective we propose a novel approach to this problem. The analysis focuses on classical integration quantifiers such as the percentage of jobs (temporary and permanent) given to immigrants, mixed marriages, and newborns with parents of mixed origin. We find that the average values of different quantifiers may exhibit either linear or non-linear growth on immigrant density and we suggest that social action, a concept identified by Max Weber, causes the observed non-linearity. Using the statistical mechanics notion of interaction to quantitatively emulate social action, a unified mathematical model for integration is proposed and it is shown to explain both growth behaviors observed. The linear theory instead, ignoring the possibility of interaction effects would underestimate the quantifiers up to 30% when immigrant densities are low, and overestimate them as much when densities are high. The capacity to quantitatively isolate different types of integration mechanisms makes our framework a suitable tool in the quest for more efficient integration policies.

A statistical mechanics approach to Granovetter theory

Science.gov (United States)

Barra, Adriano; Agliari, Elena

2012-05-01

In this paper we try to bridge breakthroughs in quantitative sociology/econometrics, pioneered during the last decades by Mac Fadden, Brock-Durlauf, Granovetter and Watts-Strogatz, by introducing a minimal model able to reproduce essentially all the features of social behavior highlighted by these authors. Our model relies on a pairwise Hamiltonian for decision-maker interactions which naturally extends the multi-populations approaches by shifting and biasing the pattern definitions of a Hopfield model of neural networks. Once introduced, the model is investigated through graph theory (to recover Granovetter and Watts-Strogatz results) and statistical mechanics (to recover Mac-Fadden and Brock-Durlauf results). Due to the internal symmetries of our model, the latter is obtained as the relaxation of a proper Markov process, allowing even to study its out-of-equilibrium properties. The method used to solve its equilibrium is an adaptation of the Hamilton-Jacobi technique recently introduced by Guerra in the spin-glass scenario and the picture obtained is the following: shifting the patterns from [-1,+1]→[0.+1] implies that the larger the amount of similarities among decision makers, the stronger their relative influence, and this is enough to explain both the different role of strong and weak ties in the social network as well as its small-world properties. As a result, imitative interaction strengths seem essentially a robust request (enough to break the gauge symmetry in the couplings), furthermore, this naturally leads to a discrete choice modelization when dealing with the external influences and to imitative behavior à la Curie-Weiss as the one introduced by Brock and Durlauf.

Statistical Thermodynamics and Microscale Thermophysics

Science.gov (United States)

Carey, Van P.

1999-08-01

Many exciting new developments in microscale engineering are based on the application of traditional principles of statistical thermodynamics. In this text Van Carey offers a modern view of thermodynamics, interweaving classical and statistical thermodynamic principles and applying them to current engineering systems. He begins with coverage of microscale energy storage mechanisms from a quantum mechanics perspective and then develops the fundamental elements of classical and statistical thermodynamics. Subsequent chapters discuss applications of equilibrium statistical thermodynamics to solid, liquid, and gas phase systems. The remainder of the book is devoted to nonequilibrium thermodynamics of transport phenomena and to nonequilibrium effects and noncontinuum behavior at the microscale. Although the text emphasizes mathematical development, Carey includes many examples and exercises to illustrate how the theoretical concepts are applied to systems of scientific and engineering interest. In the process he offers a fresh view of statistical thermodynamics for advanced undergraduate and graduate students, as well as practitioners, in mechanical, chemical, and materials engineering.

Transverse-momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in Pb+Pb collisions at √(s{sub NN}) = 2.76 TeV

Energy Technology Data Exchange (ETDEWEB)

Tripathy, Sushanta; Khuntia, Arvind; Tiwari, Swatantra Kumar; Sahoo, Raghunath [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Sciences, Indore (India)

2017-05-15

In the continuation of our previous work, the transverse-momentum (p{sub T}) spectra and nuclear modification factor (R{sub AA}) are derived using the relaxation time approximation of Boltzmann Transport Equation (BTE). The initial p{sub T}-distribution used to describe p + p collisions has been studied with the perturbative-Quantum Chromodynamics (pQCD) inspired power-law distribution, Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse-momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the p{sub T}-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at √(s{sub NN}) = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, K{sup *0} and φ. It is observed that the present formalism while explaining the transverse-momentum spectra up to 5 GeV/c, explains the nuclear modification factor very well up to 8 GeV/c in p{sub T} for all these particles except for protons. R{sub AA} is found to be independent of the degree of non-extensivity, q{sub pp} after p{sub T} ∝ 8 GeV/c. (orig.)

The statistical mechanics of vortex-acoustic ion wave turbulence

International Nuclear Information System (INIS)

Giles, M.J.

1980-01-01

The equilibrium statistical mechanics of electrostatic ion wave turbulence is studied within the framework of a continuum ion flow with adiabatic electrons. The wave field consists in general of two components, namely ion-acoustic and ion vortex modes. It is shown that the latter can significantly affect the equilibria on account of their ability both to emit and to scatter ion sound. Exact equilibria for the vortex-acoustic wave field are given in terms of a canonical distribution and the correlation functions are expressed in terms of a generating functional. Detailed calculations are carried out for the case in which the dominant coupling is an indirect interaction of the vortex modes mediated by the sound field. An equation for the spectrum of the vortex modes is obtained for this case, which is shown to possess a simple exact solution. This solution shows that the spectrum of fluctuations changes considerably as the total energy increases. Condensed vortex states could occur in the plasma sheet of the earth's magnetosphere and it is shown that the predicted ratio of the mean ion energy to the mean electron energy is consistent with the trend of observed values. (author)

Implementation of Statistical Process Control: Evaluating the Mechanical Performance of a Candidate Silicone Elastomer Docking Seal

Science.gov (United States)

Oravec, Heather Ann; Daniels, Christopher C.

2014-01-01

The National Aeronautics and Space Administration has been developing a novel docking system to meet the requirements of future exploration missions to low-Earth orbit and beyond. A dynamic gas pressure seal is located at the main interface between the active and passive mating components of the new docking system. This seal is designed to operate in the harsh space environment, but is also to perform within strict loading requirements while maintaining an acceptable level of leak rate. In this study, a candidate silicone elastomer seal was designed, and multiple subscale test articles were manufactured for evaluation purposes. The force required to fully compress each test article at room temperature was quantified and found to be below the maximum allowable load for the docking system. However, a significant amount of scatter was observed in the test results. Due to the stochastic nature of the mechanical performance of this candidate docking seal, a statistical process control technique was implemented to isolate unusual compression behavior from typical mechanical performance. The results of this statistical analysis indicated a lack of process control, suggesting a variation in the manufacturing phase of the process. Further investigation revealed that changes in the manufacturing molding process had occurred which may have influenced the mechanical performance of the seal. This knowledge improves the chance of this and future space seals to satisfy or exceed design specifications.

Statistical Physics

CERN Document Server

Wannier, Gregory Hugh

1966-01-01

Until recently, the field of statistical physics was traditionally taught as three separate subjects: thermodynamics, statistical mechanics, and kinetic theory. This text, a forerunner in its field and now a classic, was the first to recognize the outdated reasons for their separation and to combine the essentials of the three subjects into one unified presentation of thermal physics. It has been widely adopted in graduate and advanced undergraduate courses, and is recommended throughout the field as an indispensable aid to the independent study and research of statistical physics.Designed for

The nano-mechanical signature of Ultra High Performance Concrete by statistical nanoindentation techniques

International Nuclear Information System (INIS)

Sorelli, Luca; Constantinides, Georgios; Ulm, Franz-Josef; Toutlemonde, Francois

2008-01-01

Advances in engineering the microstructure of cementitious composites have led to the development of fiber reinforced Ultra High Performance Concretes (UHPC). The scope of this paper is twofold, first to characterize the nano-mechanical properties of the phases governing the UHPC microstructure by means of a novel statistical nanoindentation technique; then to upscale those nanoscale properties, by means of continuum micromechanics, to the macroscopic scale of engineering applications. In particular, a combined investigation of nanoindentation, scanning electron microscope (SEM) and X-ray Diffraction (XRD) indicates that the fiber-matrix transition zone is relatively defect free. On this basis, a four-level multiscale model with defect free interfaces allows to accurately determine the composite stiffness from the measured nano-mechanical properties. Besides evidencing the dominant role of high density calcium silicate hydrates and the stiffening effect of residual clinker, the suggested model may become a useful tool for further optimizing cement-based engineered composites

Moral foundations in an interacting neural networks society: A statistical mechanics analysis

Science.gov (United States)

Vicente, R.; Susemihl, A.; Jericó, J. P.; Caticha, N.

2014-04-01

The moral foundations theory supports that people, across cultures, tend to consider a small number of dimensions when classifying issues on a moral basis. The data also show that the statistics of weights attributed to each moral dimension is related to self-declared political affiliation, which in turn has been connected to cognitive learning styles by the recent literature in neuroscience and psychology. Inspired by these data, we propose a simple statistical mechanics model with interacting neural networks classifying vectors and learning from members of their social neighbourhood about their average opinion on a large set of issues. The purpose of learning is to reduce dissension among agents when disagreeing. We consider a family of learning algorithms parametrized by δ, that represents the importance given to corroborating (same sign) opinions. We define an order parameter that quantifies the diversity of opinions in a group with homogeneous learning style. Using Monte Carlo simulations and a mean field approximation we find the relation between the order parameter and the learning parameter δ at a temperature we associate with the importance of social influence in a given group. In concordance with data, groups that rely more strongly on corroborating evidence sustain less opinion diversity. We discuss predictions of the model and propose possible experimental tests.

Fundamental issues on kappa-distributions in space plasmas and interplanetary proton distributions

International Nuclear Information System (INIS)

Leubner, M.P.

2004-01-01

Numerous in situ observations indicate clearly the presence of nonthermal electron and ion structures as ubiquitous and persistent feature in a variety of astrophysical plasma environments. In particular, the detected suprathermal particle populations are accurately represented by the family of κ-distributions, a power-law in particle speed. After clarifying the characteristics of high-energy tail distributions under various space plasma conditions, different generation mechanisms of energetic particles are introduced where numerical simulations of wave-particle interaction based on a Fokker-Planck approach demonstrate how Landau interaction ultimately leads to κ-like distributions. Because of lack of theoretical justification, the use of the analytical form of κ-functions was frequently criticized. It is shown that these distributions turn out as consequence of an entropy generalization favored by nonextensive thermo-statistics, thus providing the missing link for powerlaw models of suprathermal tails from fundamental physics, along with a physical interpretation of the structure parameter κ. Moreover, with regard to the full nonextensive formalism, compatible also with negative values of κ, it is demonstrated that core-halo distribution structures, as observed for instance under typical interplanetary plasma conditions, are a natural content of the pseudo-additive entropy concept. The significance of the complete κ-distribution family with regard to observed core-halo electron and double-humped ion velocity space characteristics is illuminated, where the observed peak separation scale of interplanetary proton distributions is compatible with a maximum entropy condition

An Introduction to Thermodynamics and Statistical Mechanics - 2nd Edition

Science.gov (United States)

Stowe, Keith

2003-03-01

This introductory textbook for standard undergraduate courses in thermodynamics has been completely rewritten. Starting with an overview of important quantum behaviours, the book teaches students how to calculate probabilities, in order to provide a firm foundation for later chapters. It introduces the ideas of classical thermodynamics and explores them both in general and as they are applied to specific processes and interactions. The remainder of the book deals with statistical mechanics - the study of small systems interacting with huge reservoirs. The changes to this second edition have been made after more than 10 years classroom testing and student feedback. Each topic ends with a boxed summary of ideas and results, and every chapter contains numerous homework problems, covering a broad range of difficulties. Answers are given to odd numbered problems, and solutions to even problems are available to instructors at www.cambridge.org/9780521865579. The entire book has been re-written and now covers more topics It has a greater number of homework problems which range in difficulty from warm-ups to challenges It is concise and has an easy reading style

Universal biology and the statistical mechanics of early life

Science.gov (United States)

Goldenfeld, Nigel; Biancalani, Tommaso; Jafarpour, Farshid

2017-11-01

All known life on the Earth exhibits at least two non-trivial common features: the canonical genetic code and biological homochirality, both of which emerged prior to the Last Universal Common Ancestor state. This article describes recent efforts to provide a narrative of this epoch using tools from statistical mechanics. During the emergence of self-replicating life far from equilibrium in a period of chemical evolution, minimal models of autocatalysis show that homochirality would have necessarily co-evolved along with the efficiency of early-life self-replicators. Dynamical system models of the evolution of the genetic code must explain its universality and its highly refined error-minimization properties. These have both been accounted for in a scenario where life arose from a collective, networked phase where there was no notion of species and perhaps even individuality itself. We show how this phase ultimately terminated during an event sometimes known as the Darwinian transition, leading to the present epoch of tree-like vertical descent of organismal lineages. These examples illustrate concrete examples of universal biology: the quest for a fundamental understanding of the basic properties of living systems, independent of precise instantiation in chemistry or other media. This article is part of the themed issue 'Reconceptualizing the origins of life'.

Statistical mechanics and stability of random lattice field theory

International Nuclear Information System (INIS)

Baskaran, G.

1984-01-01

The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities. (orig.)

Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model

International Nuclear Information System (INIS)

Ng, Felix S.L.

2016-01-01

We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE's solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.

Statistical characteristics of mechanical heart valve cavitation in accelerated testing.

Science.gov (United States)

Wu, Changfu; Hwang, Ned H C; Lin, Yu-Kweng M

2004-07-01

Cavitation damage has been observed on mechanical heart valves (MHVs) undergoing accelerated testing. Cavitation itself can be modeled as a stochastic process, as it varies from beat to beat of the testing machine. This in-vitro study was undertaken to investigate the statistical characteristics of MHV cavitation. A 25-mm St. Jude Medical bileaflet MHV (SJM 25) was tested in an accelerated tester at various pulse rates, ranging from 300 to 1,000 bpm, with stepwise increments of 100 bpm. A miniature pressure transducer was placed near a leaflet tip on the inflow side of the valve, to monitor regional transient pressure fluctuations at instants of valve closure. The pressure trace associated with each beat was passed through a 70 kHz high-pass digital filter to extract the high-frequency oscillation (HFO) components resulting from the collapse of cavitation bubbles. Three intensity-related measures were calculated for each HFO burst: its time span; its local root-mean-square (LRMS) value; and the area enveloped by the absolute value of the HFO pressure trace and the time axis, referred to as cavitation impulse. These were treated as stochastic processes, of which the first-order probability density functions (PDFs) were estimated for each test rate. Both the LRMS value and cavitation impulse were log-normal distributed, and the time span was normal distributed. These distribution laws were consistent at different test rates. The present investigation was directed at understanding MHV cavitation as a stochastic process. The results provide a basis for establishing further the statistical relationship between cavitation intensity and time-evolving cavitation damage on MHV surfaces. These data are required to assess and compare the performance of MHVs of different designs.

The role of angular momentum conservation law in statistical mechanics

Directory of Open Access Journals (Sweden)

I.M. Dubrovskii

2008-12-01

Full Text Available Within the limits of Khinchin ideas [A.Y. Khinchin, Mathematical Foundation of Statistical Mechanics. NY, Ed. Dover, 1949] the importance of momentum and angular momentum conservation laws was analyzed for two cases: for uniform magnetic field and when magnetic field is absent. The law of momentum conservation does not change the density of probability distribution in both cases, just as it is assumed in the conventional theory. It is shown that in systems where the kinetic energy depends only on particle momenta canonically conjugated with Cartesian coordinates being their diagonal quadric form,the angular momentum conservation law changes the density of distribution of the system only in case the full angular momentum of a system is not equal to zero. In the gas of charged particles in a uniform magnetic field the density of distribution also varies if the angular momentum is zero [see Dubrovskii I.M., Condensed Matter Physics, 2206, 9, 23]. Two-dimensional gas of charged particles located within a section of an endless strip filled with gas in magnetic field is considered. Under such conditions the angular momentum is not conserved. Directional particle flows take place close to the strip boundaries, and, as a consequence, the phase trajectory of the considered set of particles does not remain within the limited volume of the phase space. In order to apply a statistical thermodynamics method, it was suggested to consider near-boundary trajectories relative to a reference system that moves uniformly. It was shown that if the diameter of an orbit having average thermal energy is much smaller than a strip width, the corrections to thermodynamic functions are small depending on magnetic field. Only the average velocity of near-boundary particles that form near-boundary electric currents creating the paramagnetic moment turn out to be essential.

Statistical evaluation of the mechanical properties of high-volume class F fly ash concretes

KAUST Repository

Yoon, Seyoon

2014-03-01

High-Volume Fly Ash (HVFA) concretes are seen by many as a feasible solution for sustainable, low embodied carbon construction. At the moment, fly ash is classified as a waste by-product, primarily of thermal power stations. In this paper the authors experimentally and statistically investigated the effects of mix-design factors on the mechanical properties of high-volume class F fly ash concretes. A total of 240 and 32 samples were produced and tested in the laboratory to measure compressive strength and Young\\'s modulus respectively. Applicability of the CEB-FIP (Comite Euro-international du Béton - Fédération Internationale de la Précontrainte) and ACI (American Concrete Institute) Building Model Code (Thomas, 2010; ACI Committee 209, 1982) [1,2] to the experimentally-derived mechanical property data for HVFA concretes was established. Furthermore, using multiple linear regression analysis, Mean Squared Residuals (MSRs) were obtained to determine whether a weight- or volume-based mix proportion is better to predict the mechanical properties of HVFA concrete. The significance levels of the design factors, which indicate how significantly the factors affect the HVFA concrete\\'s mechanical properties, were determined using analysis of variance (ANOVA) tests. The results show that a weight-based mix proportion is a slightly better predictor of mechanical properties than volume-based one. The significance level of fly ash substitution rate was higher than that of w/b ratio initially but reduced over time. © 2014 Elsevier Ltd. All rights reserved.

A statistical model of uplink inter-cell interference with slow and fast power control mechanisms

KAUST Repository

Tabassum, Hina; Yilmaz, Ferkan; Dawy, Zaher; Alouini, Mohamed-Slim

2013-01-01

Uplink power control is in essence an interference mitigation technique that aims at minimizing the inter-cell interference (ICI) in cellular networks by reducing the transmit power levels of the mobile users while maintaining their target received signal quality levels at base stations. Power control mechanisms directly impact the interference dynamics and, thus, affect the overall achievable capacity and consumed power in cellular networks. Due to the stochastic nature of wireless channels and mobile users' locations, it is important to derive theoretical models for ICI that can capture the impact of design alternatives related to power control mechanisms. To this end, we derive and verify a novel statistical model for uplink ICI in Generalized-K composite fading environments as a function of various slow and fast power control mechanisms. The derived expressions are then utilized to quantify numerically key network performance metrics that include average resource fairness, average reduction in power consumption, and ergodic capacity. The accuracy of the derived expressions is validated via Monte-Carlo simulations. Results are generated for multiple network scenarios, and insights are extracted to assess various power control mechanisms as a function of system parameters. © 1972-2012 IEEE.

A statistical model of uplink inter-cell interference with slow and fast power control mechanisms

KAUST Repository

Tabassum, Hina

2013-09-01

Uplink power control is in essence an interference mitigation technique that aims at minimizing the inter-cell interference (ICI) in cellular networks by reducing the transmit power levels of the mobile users while maintaining their target received signal quality levels at base stations. Power control mechanisms directly impact the interference dynamics and, thus, affect the overall achievable capacity and consumed power in cellular networks. Due to the stochastic nature of wireless channels and mobile users\\' locations, it is important to derive theoretical models for ICI that can capture the impact of design alternatives related to power control mechanisms. To this end, we derive and verify a novel statistical model for uplink ICI in Generalized-K composite fading environments as a function of various slow and fast power control mechanisms. The derived expressions are then utilized to quantify numerically key network performance metrics that include average resource fairness, average reduction in power consumption, and ergodic capacity. The accuracy of the derived expressions is validated via Monte-Carlo simulations. Results are generated for multiple network scenarios, and insights are extracted to assess various power control mechanisms as a function of system parameters. © 1972-2012 IEEE.

Semiclassical analysis, Witten Laplacians, and statistical mechanis

CERN Document Server

Helffer, Bernard

2002-01-01

This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality. Contents: Witten Laplacians Approach; Problems in Statistical Mechanics with Discrete Spins; Laplace Integrals and Transfer Operators; S

Ants in a labyrinth: a statistical mechanics approach to the division of labour.

Directory of Open Access Journals (Sweden)

Thomas Owen Richardson

2011-04-01

Full Text Available Division of labour (DoL is a fundamental organisational principle in human societies, within virtual and robotic swarms and at all levels of biological organisation. DoL reaches a pinnacle in the insect societies where the most widely used model is based on variation in response thresholds among individuals, and the assumption that individuals and stimuli are well-mixed. Here, we present a spatially explicit model of DoL. Our model is inspired by Pierre de Gennes' 'Ant in a Labyrinth' which laid the foundations of an entire new field in statistical mechanics. We demonstrate the emergence, even in a simplified one-dimensional model, of a spatial patterning of individuals and a right-skewed activity distribution, both of which are characteristics of division of labour in animal societies. We then show using a two-dimensional model that the work done by an individual within an activity bout is a sigmoidal function of its response threshold. Furthermore, there is an inverse relationship between the overall stimulus level and the skewness of the activity distribution. Therefore, the difference in the amount of work done by two individuals with different thresholds increases as the overall stimulus level decreases. Indeed, spatial fluctuations of task stimuli are minimised at these low stimulus levels. Hence, the more unequally labour is divided amongst individuals, the greater the ability of the colony to maintain homeostasis. Finally, we show that the non-random spatial distribution of individuals within biological and social systems could be caused by indirect (stigmergic interactions, rather than direct agent-to-agent interactions. Our model links the principle of DoL with principles in the statistical mechanics and provides testable hypotheses for future experiments.

Statistical mechanics of a one-component fluid of charged hard rods in 1D

International Nuclear Information System (INIS)

Vericat, F.; Blum, L.

1986-09-01

The statistical mechanics of a classical one component system of charged hard rods in a neutralizing background is investigated in 1D stressing on the effects of the hard core interactions over the thermodynamic and the structure of the system. The crystalline status of the system at all temperatures and densities and the absence of phase transitions is shown by extending previous results of Baxter and Kunz on the one-component plasma of point particles. Explicit expressions for the thermodynamic functions and the one-particle correlation function are given in the limits of small and strong couplings. (author)

Concept of probability in statistical physics

CERN Document Server

Guttmann, Y M

1999-01-01

Foundational issues in statistical mechanics and the more general question of how probability is to be understood in the context of physical theories are both areas that have been neglected by philosophers of physics. This book fills an important gap in the literature by providing a most systematic study of how to interpret probabilistic assertions in the context of statistical mechanics. The book explores both subjectivist and objectivist accounts of probability, and takes full measure of work in the foundations of probability theory, in statistical mechanics, and in mathematical theory. It will be of particular interest to philosophers of science, physicists and mathematicians interested in foundational issues, and also to historians of science.

Statistical Analysis of Categorical Time Series of Atmospheric Elementary Circulation Mechanisms - Dzerdzeevski Classification for the Northern Hemisphere.

Science.gov (United States)

Brenčič, Mihael

2016-01-01

Northern hemisphere elementary circulation mechanisms, defined with the Dzerdzeevski classification and published on a daily basis from 1899-2012, are analysed with statistical methods as continuous categorical time series. Classification consists of 41 elementary circulation mechanisms (ECM), which are assigned to calendar days. Empirical marginal probabilities of each ECM were determined. Seasonality and the periodicity effect were investigated with moving dispersion filters and randomisation procedure on the ECM categories as well as with the time analyses of the ECM mode. The time series were determined as being non-stationary with strong time-dependent trends. During the investigated period, periodicity interchanges with periods when no seasonality is present. In the time series structure, the strongest division is visible at the milestone of 1986, showing that the atmospheric circulation pattern reflected in the ECM has significantly changed. This change is result of the change in the frequency of ECM categories; before 1986, the appearance of ECM was more diverse, and afterwards fewer ECMs appear. The statistical approach applied to the categorical climatic time series opens up new potential insight into climate variability and change studies that have to be performed in the future.

Statistical mechanics of polymer networks of any topology

International Nuclear Information System (INIS)

Duplantier, B.

1989-01-01

The statistical mechanics is considered of any polymer network with a prescribed topology, in dimension d, which was introduced previously. The basic direct renormalization theory of the associated continuum model is established. It has a very simple multiplicative structure in terms of the partition functions of the star polymers constituting the vertices of the network. A calculation is made to O(ε 2 ), where d = 4 -ε, of the basic critical dimensions σ L associated with any L=leg vertex (L ≥ 1). From this infinite series of critical exponents, any topology-dependent critical exponent can be derived. This is applied to the configuration exponent γ G of any network G to O(ε 2 ), including L-leg star polymers. The infinite sets of contact critical exponents θ between multiple points of polymers or between the cores of several star polymers are also deduced. As a particular case, the three exponents θ 0 , θ 1 , θ 2 calculated by des Cloizeaux by field-theoretic methods are recovered. The limiting exact logarithmic laws are derived at the upper critical dimension d = 4. The results are generalized to the series of topological exponents of polymer networks near a surface and of tricritical polymers at the Θ-point. Intersection properties of networks of random walks can be studied similarly. The above factorization theory of the partition function of any polymer network over its constituting L-vertices also applies to two dimensions, where it can be related to conformal invariance. The basic critical exponents σ L and thus any topological polymer exponents are then exactly known. Principal results published elsewhere are recalled

Statistical mechanics of microscopically thin thermalized shells

Science.gov (United States)

Kosmrlj, Andrej

Recent explosion in fabrication of microscopically thin free standing structures made from graphene and other two-dimensional materials has led to a renewed interest in the mechanics of such structures in presence of thermal fluctuations. Since late 1980s it has been known that for flat solid sheets thermal fluctuations effectively increase the bending rigidity and reduce the bulk and shear moduli in a scale-dependent fashion. However, much is still unknown about the mechanics of thermalized flat sheets of complex geometries and about the mechanics of thermalized shells with non-zero background curvature. In this talk I will present recent development in the mechanics of thermalized ribbons, spherical shells and cylindrical tubes. Long ribbons are found to behave like hybrids between flat sheets with renormalized elastic constants and semi-flexible polymers, and these results can be used to predict the mechanics of graphene kirigami structures. Contrary to the anticipated behavior for ribbons, the non-zero background curvature of shells leads to remarkable novel phenomena. In shells, thermal fluctuations effectively generate negative surface tension, which can significantly reduce the critical buckling pressure for spherical shells and the critical axial load for cylindrical tubes. For large shells this thermally generated load becomes big enough to spontaneously crush spherical shells and cylindrical tubes even in the absence of external loads. I will comment on the relevance for crushing of microscopic shells (viral capsids, bacteria, microcapsules) due to osmotic shocks and for crushing of nanotubes.

Probability and logical structure of statistical theories

International Nuclear Information System (INIS)

Hall, M.J.W.

1988-01-01

A characterization of statistical theories is given which incorporates both classical and quantum mechanics. It is shown that each statistical theory induces an associated logic and joint probability structure, and simple conditions are given for the structure to be of a classical or quantum type. This provides an alternative for the quantum logic approach to axiomatic quantum mechanics. The Bell inequalities may be derived for those statistical theories that have a classical structure and satisfy a locality condition weaker than factorizability. The relation of these inequalities to the issue of hidden variable theories for quantum mechanics is discussed and clarified

Exact results in nonequilibrium statistical mechanics: Formalism and applications in chemical kinetics and single-molecule free energy estimation

Science.gov (United States)

Adib, Artur B.

In the last two decades or so, a collection of results in nonequilibrium statistical mechanics that departs from the traditional near-equilibrium framework introduced by Lars Onsager in 1931 has been derived, yielding new fundamental insights into far-from-equilibrium processes in general. Apart from offering a more quantitative statement of the second law of thermodynamics, some of these results---typified by the so-called "Jarzynski equality"---have also offered novel means of estimating equilibrium quantities from nonequilibrium processes, such as free energy differences from single-molecule "pulling" experiments. This thesis contributes to such efforts by offering three novel results in nonequilibrium statistical mechanics: (a) The entropic analog of the Jarzynski equality; (b) A methodology for estimating free energies from "clamp-and-release" nonequilibrium processes; and (c) A directly measurable symmetry relation in chemical kinetics similar to (but more general than) chemical detailed balance. These results share in common the feature of remaining valid outside Onsager's near-equilibrium regime, and bear direct applicability in protein folding kinetics as well as in single-molecule free energy estimation.

Statistical mechanics of binary mixture adsorption in metal-organic frameworks in the osmotic ensemble

Science.gov (United States)

Dunne, Lawrence J.; Manos, George

2018-03-01

Although crucial for designing separation processes little is known experimentally about multi-component adsorption isotherms in comparison with pure single components. Very few binary mixture adsorption isotherms are to be found in the literature and information about isotherms over a wide range of gas-phase composition and mechanical pressures and temperature is lacking. Here, we present a quasi-one-dimensional statistical mechanical model of binary mixture adsorption in metal-organic frameworks (MOFs) treated exactly by a transfer matrix method in the osmotic ensemble. The experimental parameter space may be very complex and investigations into multi-component mixture adsorption may be guided by theoretical insights. The approach successfully models breathing structural transitions induced by adsorption giving a good account of the shape of adsorption isotherms of CO2 and CH4 adsorption in MIL-53(Al). Binary mixture isotherms and co-adsorption-phase diagrams are also calculated and found to give a good description of the experimental trends in these properties and because of the wide model parameter range which reproduces this behaviour suggests that this is generic to MOFs. Finally, a study is made of the influence of mechanical pressure on the shape of CO2 and CH4 adsorption isotherms in MIL-53(Al). Quite modest mechanical pressures can induce significant changes to isotherm shapes in MOFs with implications for binary mixture separation processes. This article is part of the theme issue `Modern theoretical chemistry'.

Entropic lattice Boltzmann representations required to recover Navier-Stokes flows.

Science.gov (United States)

Keating, Brian; Vahala, George; Yepez, Jeffrey; Soe, Min; Vahala, Linda

2007-03-01

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in Tsallis-like forms. However, with the imposition of the pressure tensor moment constraint, as is fundamentally necessary for the recovery of the Navier-Stokes equations, it is proved that the entropy function must be of the discrete Boltzmann form. Three-dimensional simulations are performed which illustrate some of the differences between standard lattice Boltzmann and entropic lattice Boltzmann schemes, as well as the role played by the number of phase-space velocities used in the discretization.

The determinants of bond angle variability in protein/peptide backbones: A comprehensive statistical/quantum mechanics analysis.

Science.gov (United States)

Improta, Roberto; Vitagliano, Luigi; Esposito, Luciana

2015-11-01

The elucidation of the mutual influence between peptide bond geometry and local conformation has important implications for protein structure refinement, validation, and prediction. To gain insights into the structural determinants and the energetic contributions associated with protein/peptide backbone plasticity, we here report an extensive analysis of the variability of the peptide bond angles by combining statistical analyses of protein structures and quantum mechanics calculations on small model peptide systems. Our analyses demonstrate that all the backbone bond angles strongly depend on the peptide conformation and unveil the existence of regular trends as function of ψ and/or φ. The excellent agreement of the quantum mechanics calculations with the statistical surveys of protein structures validates the computational scheme here employed and demonstrates that the valence geometry of protein/peptide backbone is primarily dictated by local interactions. Notably, for the first time we show that the position of the H(α) hydrogen atom, which is an important parameter in NMR structural studies, is also dependent on the local conformation. Most of the trends observed may be satisfactorily explained by invoking steric repulsive interactions; in some specific cases the valence bond variability is also influenced by hydrogen-bond like interactions. Moreover, we can provide a reliable estimate of the energies involved in the interplay between geometry and conformations. © 2015 Wiley Periodicals, Inc.

Mathematics of statistical mechanics and the chaos theory; Las matematicas de la mecanica estadistica y de la teoria del caos

Energy Technology Data Exchange (ETDEWEB)

Llave, R. de la; Haro, A.

2000-07-01

Statistical mechanics requires a language that unifies probabilistic and deterministic description of physical systems. We describe briefly some of the mathematical ideas needed for this unification. These ideas have also proved important in the study of chaotic systems. (Author) 17 refs.

Physics colloquium: Single-electron counting in quantum metrology and in statistical mechanics

CERN Multimedia

Geneva University

2011-01-01

GENEVA UNIVERSITY Ecole de physique Département de physique nucléaire et corspusculaire 24, quai Ernest-Ansermet 1211 Genève 4 Tél.: (022) 379 62 73 Fax: (022) 379 69 92olé   Lundi 17 octobre 2011 17h00 - Ecole de Physique, Auditoire Stueckelberg PHYSICS COLLOQUIUM « Single-electron counting in quantum metrology and in statistical mechanics » Prof. Jukka Pekola Low Temperature Laboratory, Aalto University Helsinki, Finland   First I discuss the basics of single-electron tunneling and its potential applications in metrology. My main focus is in developing an accurate source of single-electron current for the realization of the unit ampere. I discuss the principle and the present status of the so-called single- electron turnstile. Investigation of errors in transporting electrons one by one has revealed a wealth of observations on fundamental phenomena in mesoscopic superconductivity, including individual Andreev...

Maximum entropy principle and hydrodynamic models in statistical mechanics

International Nuclear Information System (INIS)

Trovato, M.; Reggiani, L.

2012-01-01

This review presents the state of the art of the maximum entropy principle (MEP) in its classical and quantum (QMEP) formulation. Within the classical MEP we overview a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport in the presence of electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. Analogously, the theoretical approach is applied to many one-dimensional n + nn + submicron Si structures by using different band structure models, different doping profiles, different applied biases and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with available experimental data. Within the quantum MEP we introduce a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is then asserted as fundamental principle of quantum statistical mechanics. Accordingly, we have developed a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theory is formulated both in thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ħ 2 , being ħ the reduced Planck constant. In particular, by using an arbitrary number of moments, we prove that: i) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives both of the

Essays on the statistical mechanics of the labor market and implications for the distribution of earned income

Science.gov (United States)

Schneider, Markus P. A.

This dissertation contributes to two areas in economics: the understanding of the distribution of earned income and to Bayesian analysis of distributional data. Recently, physicists claimed that the distribution of earned income is exponential (see Yakovenko, 2009). The first chapter explores the perspective that the economy is a statistical mechanical system and the implication for labor market outcomes is considered critically. The robustness of the empirical results that lead to the physicists' claims, the significance of the exponential distribution in statistical mechanics, and the case for a conservation law in economics are discussed. The conclusion reached is that physicists' conception of the economy is too narrow even within their chosen framework, but that their overall approach is insightful. The dual labor market theory of segmented labor markets is invoked to understand why the observed distribution may be a mixture of distributional components, corresponding to different generating mechanisms described in Reich et al. (1973). The application of informational entropy in chapter II connects this work to Bayesian analysis and maximum entropy econometrics. The analysis follows E. T. Jaynes's treatment of Wolf's dice data, but is applied to the distribution of earned income based on CPS data. The results are calibrated to account for rounded survey responses using a simple simulation, and answer the graphical analyses by physicists. The results indicate that neither the income distribution of all respondents nor of the subpopulation used by physicists appears to be exponential. The empirics do support the claim that a mixture with exponential and log-normal distributional components ts the data. In the final chapter, a log-linear model is used to fit the exponential to the earned income distribution. Separating the CPS data by gender and marital status reveals that the exponential is only an appropriate model for a limited number of subpopulations, namely

A Simulational approach to teaching statistical mechanics and kinetic theory

International Nuclear Information System (INIS)

Karabulut, H.

2005-01-01

A computer simulation demonstrating how Maxwell-Boltzmann distribution is reached in gases from a nonequilibrium distribution is presented. The algorithm can be generalized to the cases of gas particles (atoms or molecules) with internal degrees of freedom such as electronic excitations and vibrational-rotational energy levels. Another generalization of the algorithm is the case of mixture of two different gases. By choosing the collision cross sections properly one can create quasi equilibrium distributions. For example by choosing same atom cross sections large and different atom cross sections very small one can create mixture of two gases with different temperatures where two gases slowly interact and come to equilibrium in a long time. Similarly, for the case one kind of atom with internal degrees of freedom one can create situations that internal degrees of freedom come to the equilibrium much later than translational degrees of freedom. In all these cases the equilibrium distribution that the algorithm gives is the same as expected from the statistical mechanics. The algorithm can also be extended to cover the case of chemical equilibrium where species A and B react to form AB molecules. The laws of chemical equilibrium can be observed from this simulation. The chemical equilibrium simulation can also help to teach the elusive concept of chemical potential

Statistical mechanics of reacting dense plasmas

Energy Technology Data Exchange (ETDEWEB)

Rogers, F.J.

1978-11-22

A review of the quantum statistical theory of strongly coupled many component plasmas is given. The theoretical development is shown to consist of six separate parts. Compensation between bound and scattering state contributions to the partition function and use of the shifted Debye energy levels are important aspects of the analysis. The results are valid when the electrons are moderately coupled to the heavy ions, i.e., ..lambda../sub e..cap alpha../* < 1, but no restriction is placed on the coupling between heavy ions. Another restriction is that lambda/lambda/sub D/ < 1, i.e., the thermal deBroglie wavelength is less than the Debye length. Numerical calculations of PV/N/sub 0/kT and C/sub V/ are given for a Rubidium plasma.

Applied statistics for economists

CERN Document Server

Lewis, Margaret

2012-01-01

This book is an undergraduate text that introduces students to commonly-used statistical methods in economics. Using examples based on contemporary economic issues and readily-available data, it not only explains the mechanics of the various methods, it also guides students to connect statistical results to detailed economic interpretations. Because the goal is for students to be able to apply the statistical methods presented, online sources for economic data and directions for performing each task in Excel are also included.

Applied statistical thermodynamics

CERN Document Server

Lucas, Klaus

1991-01-01

The book guides the reader from the foundations of statisti- cal thermodynamics including the theory of intermolecular forces to modern computer-aided applications in chemical en- gineering and physical chemistry. The approach is new. The foundations of quantum and statistical mechanics are presen- ted in a simple way and their applications to the prediction of fluid phase behavior of real systems are demonstrated. A particular effort is made to introduce the reader to expli- cit formulations of intermolecular interaction models and to show how these models influence the properties of fluid sy- stems. The established methods of statistical mechanics - computer simulation, perturbation theory, and numerical in- tegration - are discussed in a style appropriate for newcom- ers and are extensively applied. Numerous worked examples illustrate how practical calculations should be carried out.

A Framework for Structural Systems Based on the Principles of Statistical Mechanics

Directory of Open Access Journals (Sweden)

Rabindranath Andujar

2014-11-01

Full Text Available A framework is proposed in which certain well-known concepts of statistical mechanics and thermodynamics can be used and applied to characterize structural systems of interconnected Timoshenko beam elements. We first make the assimilation to a network of nodes linked by potential energy functions that are derived from the stiffness properties of the beams. Then we define a series of thermodynamic quantities inherent to a given structure (i.e., internal energy, heat, pressure, temperature, entropy, and kinetic energy. With the exception of entropy, all of them have the dimensions of energy. In order to test this new framework, a series of experiments was performed on four structural specimens within the elastic regime. Their configurations were taken from the seismic regulations known as Eurocode 8 in order to have a better based reference for our comparisons. The results are then explained within this new framework. Very interesting correlations have been found between the parameters given in the code and our concepts.

Statistical mechanical model of gas adsorption in porous crystals with dynamic moieties.

Science.gov (United States)

Simon, Cory M; Braun, Efrem; Carraro, Carlo; Smit, Berend

2017-01-17

Some nanoporous, crystalline materials possess dynamic constituents, for example, rotatable moieties. These moieties can undergo a conformation change in response to the adsorption of guest molecules, which qualitatively impacts adsorption behavior. We pose and solve a statistical mechanical model of gas adsorption in a porous crystal whose cages share a common ligand that can adopt two distinct rotational conformations. Guest molecules incentivize the ligands to adopt a different rotational configuration than maintained in the empty host. Our model captures inflections, steps, and hysteresis that can arise in the adsorption isotherm as a signature of the rotating ligands. The insights disclosed by our simple model contribute a more intimate understanding of the response and consequence of rotating ligands integrated into porous materials to harness them for gas storage and separations, chemical sensing, drug delivery, catalysis, and nanoscale devices. Particularly, our model reveals design strategies to exploit these moving constituents and engineer improved adsorbents with intrinsic thermal management for pressure-swing adsorption processes.

Statistical Physics

CERN Document Server

Mandl, Franz

1988-01-01

The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition E. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient

Dust-acoustic waves and stability in the permeating dusty plasma. II. Power-law distributions

International Nuclear Information System (INIS)

Gong Jingyu; Du Jiulin; Liu Zhipeng

2012-01-01

The dust-acoustic waves and the stability theory for the permeating dusty plasma with power-law distributions are studied by using nonextensive q-statistics. In two limiting physical cases, when the thermal velocity of the flowing dusty plasma is much larger than, and much smaller than the phase velocity of the waves, we derived the dust-acoustic wave frequency, the instability growth rate, and the instability critical flowing velocity. As compared with the formulae obtained in part I [Gong et al., Phys. Plasmas 19, 043704 (2012)], all formulae of the present cases and the resulting plasma characteristics are q-dependent, and the power-law distribution of each plasma component of the permeating dusty plasma has a different q-parameter and thus has a different nonextensive effect. Further, we make numerical analyses of an example that a cometary plasma tail is passing through the interplanetary space dusty plasma and we show that these power-law distributions have significant effects on the plasma characteristics of this kind of plasma environment.

An introduction to statistical thermodynamics

CERN Document Server

Hill, Terrell L

1987-01-01

""A large number of exercises of a broad range of difficulty make this book even more useful…a good addition to the literature on thermodynamics at the undergraduate level."" - Philosophical MagazineAlthough written on an introductory level, this wide-ranging text provides extensive coverage of topics of current interest in equilibrium statistical mechanics. Indeed, certain traditional topics are given somewhat condensed treatment to allow room for a survey of more recent advances.The book is divided into four major sections. Part I deals with the principles of quantum statistical mechanics a

Theoretical physics vol. 2. Quantum mechanics, relativistic quantum mechanics, quantum field theory, elementar-particle theory, thermodynamics and statistics

International Nuclear Information System (INIS)

Rebhan, E.

2005-01-01

The present second volume treats quantum mechanics, relativistic quantum mechanics, the foundations of quantum-field and elementary-particle theory as well as thermodynamics and statistics. Both volumes comprehend all fields, which are usually offered in a course about theoretical physics. In all treated fields a very careful introduction to the basic natural laws forms the starting point, whereby it is thoroughly analysed, which of them is based on empirics, which is logically deducible, and which role play basic definitions. Extendingly the matter extend of the corresponding courses starting from the relativistic quantum theory an introduction to the elementary particles is developed. All problems are very thoroughly and such extensively studied, that each step is singularly reproducible. On motivation and good understandability is cared much about. The mixing of mathematical difficulties with problems of physical nature often obstructive in the learning is so circumvented, that important mathematical methods are presented in own chapters (for instance Hilbert spaces, Lie groups). By means of many examples and problems (for a large part with solutions) the matter worked out is deepened and exercised. Developments, which are indeed important, but seem for the first approach abandonable, are pursued in excurses. This book starts from courses, which the author has held at the Heinrich-Heine university in Duesseldorf, and was in many repetitions fitted to the requirements of the students. It is conceived in such a way, that it is also after the study suited as dictionary or for the regeneration

Quantum formalism for classical statistics

Science.gov (United States)

Wetterich, C.

2018-06-01

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

Co-Evolutionary Mechanisms of Emotional Bursts in Online Social Dynamics and Networks

Directory of Open Access Journals (Sweden)

Bosiljka Tadić

2013-11-01

Full Text Available Collective emotional behavior of users is frequently observed on various Web portals; however, its complexity and the role of emotions in the acting mechanisms are still not thoroughly understood. In this work, using the empirical data and agent-based modeling, a parallel analysis is performed of two archetypal systems—Blogs and Internet-Relayed-Chats—both of which maintain self-organized dynamics but not the same communication rules and time scales. The emphasis is on quantifying the collective emotions by means of fractal analysis of the underlying processes as well as topology of social networks, which arise and co-evolve in these stochastic processes. The results reveal that two distinct mechanisms, which are based on different use of emotions (an emotion is characterized by two components, arousal and valence, are intrinsically associated with two classes of emergent social graphs. Their hallmarks are the evolution of communities in accordance with the excess of the negative emotions on popular Blogs, on one side, and smooth spreading of the Bot’s emotional impact over the entire hierarchical network of chats, on the other. Another emphasis of this work is on the understanding of nonextensivity of the emotion dynamics; it was found that, in its own way, each mechanism leads to a reduced phase space of the emotion components when the collective dynamics takes place. That a non-additive entropy describes emotion dynamics, is further confirmed by computing the q-generalized Kolmogorov-Sinai entropy rate in the empirical data of chats as well as in the simulations of interacting emotional agents and Bots.

A statistical mechanical model for equilibrium ionization

International Nuclear Information System (INIS)

Macris, N.; Martin, P.A.; Pule, J.

1990-01-01

A quantum electron interacts with a classical gas of hard spheres and is in thermal equilibrium with it. The interaction is attractive and the electron can form a bound state with the classical particles. It is rigorously shown that in a well defined low density and low temperature limit, the ionization probability for the electron tends to the value predicted by the Saha formula for thermal ionization. In this regime, the electron is found to be in a statistical mixture of a bound and a free state. (orig.)

Statistical Description of Segregation in a Powder Mixture

DEFF Research Database (Denmark)

Chapiro, Alexander; Stenby, Erling Halfdan

1996-01-01

In this paper we apply the statistical mechanics of powders to describe a segregated state in a mixture of grains of different sizes. Variation of the density of a packing with depth arising due to changes of particle configurations is studied. The statistical mechanics of powders is generalized...

Statistical model for the mechanical behavior of the tissue engineering non-woven fibrous matrices under large deformation.

Science.gov (United States)

Rizvi, Mohd Suhail; Pal, Anupam

2014-09-01

The fibrous matrices are widely used as scaffolds for the regeneration of load-bearing tissues due to their structural and mechanical similarities with the fibrous components of the extracellular matrix. These scaffolds not only provide the appropriate microenvironment for the residing cells but also act as medium for the transmission of the mechanical stimuli, essential for the tissue regeneration, from macroscopic scale of the scaffolds to the microscopic scale of cells. The requirement of the mechanical loading for the tissue regeneration requires the fibrous scaffolds to be able to sustain the complex three-dimensional mechanical loading conditions. In order to gain insight into the mechanical behavior of the fibrous matrices under large amount of elongation as well as shear, a statistical model has been formulated to study the macroscopic mechanical behavior of the electrospun fibrous matrix and the transmission of the mechanical stimuli from scaffolds to the cells via the constituting fibers. The study establishes the load-deformation relationships for the fibrous matrices for different structural parameters. It also quantifies the changes in the fiber arrangement and tension generated in the fibers with the deformation of the matrix. The model reveals that the tension generated in the fibers on matrix deformation is not homogeneous and hence the cells located in different regions of the fibrous scaffold might experience different mechanical stimuli. The mechanical response of fibrous matrices was also found to be dependent on the aspect ratio of the matrix. Therefore, the model establishes a structure-mechanics interdependence of the fibrous matrices under large deformation, which can be utilized in identifying the appropriate structure and external mechanical loading conditions for the regeneration of load-bearing tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.

Counting in Lattices: Combinatorial Problems from Statistical Mechanics.

Science.gov (United States)

Randall, Dana Jill

In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and self-avoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in higher dimensional lattices. We present the first efficient approximation algorithm for computing the number of matchings of any size in any periodic lattice in arbitrary dimension. The algorithm is based on Monte Carlo simulation of a suitable Markov chain and has rigorously derived performance guarantees that do not rely on any assumptions. In addition, we show that these results generalize to counting matchings in any graph which is the Cayley graph of a finite group. The second problem is counting self-avoiding walks in lattices. This problem arises in the study of the thermodynamics of long polymer chains in dilute solution. While there are a number of Monte Carlo algorithms used to count self -avoiding walks in practice, these are heuristic and their correctness relies on unproven conjectures. In contrast, we present an efficient algorithm which relies on a single, widely-believed conjecture that is simpler than preceding assumptions and, more importantly, is one which the algorithm itself can test. Thus our algorithm is reliable, in the sense that it either outputs answers that are guaranteed, with high probability, to be correct, or finds a counterexample to the conjecture. In either case we know we can trust our results and the algorithm is guaranteed to run in polynomial time. This is the first algorithm for counting self-avoiding walks in which the error bounds are rigorously controlled. This work was supported in part by an AT&T graduate fellowship, a University of

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.

Science.gov (United States)

Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray

2014-05-13

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.

Small amplitude two dimensional electrostatic excitations in a magnetized dusty plasma with q-distributed electrons

Science.gov (United States)

Khan, Shahab Ullah; Adnan, Muhammad; Qamar, Anisa; Mahmood, Shahzad

2016-07-01

The propagation of linear and nonlinear electrostatic waves is investigated in magnetized dusty plasma with stationary negatively or positively charged dust, cold mobile ions and non-extensive electrons. Two normal modes are predicted in the linear regime, whose characteristics are investigated parametrically, focusing on the effect of electrons non-extensivity, dust charge polarity, concentration of dust and magnetic field strength. Using the reductive perturbation technique, a Zakharov-Kuznetsov (ZK) type equation is derived which governs the dynamics of small-amplitude solitary waves in magnetized dusty plasma. The properties of the solitary wave structures are analyzed numerically with the system parameters i.e. electrons non-extensivity, concentration of dust, polarity of dust and magnetic field strength. Following Allen and Rowlands (J. Plasma Phys. 53:63, 1995), we have shown that the pulse soliton solution of the ZK equation is unstable, and have analytically traced the dependence of the instability growth rate on the nonextensive parameter q for electrons, dust charge polarity and magnetic field strength. The results should be useful for understanding the nonlinear propagation of DIA solitary waves in laboratory and space plasmas.

Elements of statistical thermodynamics

CERN Document Server

Nash, Leonard K

2006-01-01

Encompassing essentially all aspects of statistical mechanics that appear in undergraduate texts, this concise, elementary treatment shows how an atomic-molecular perspective yields new insights into macroscopic thermodynamics. 1974 edition.

Elementary statistical physics

CERN Document Server

Kittel, C

1965-01-01

This book is intended to help physics students attain a modest working knowledge of several areas of statistical mechanics, including stochastic processes and transport theory. The areas discussed are among those forming a useful part of the intellectual background of a physicist.

Thermodynamic geometry for a non-extensive ideal gas

Science.gov (United States)

López, J. L.; Obregón, O.; Torres-Arenas, J.

2018-05-01

A generalized entropy arising in the context of superstatistics is applied to an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric approach to thermodynamics. By means of the curvature/interaction hypothesis of the geometric approach to thermodynamic geometry it is found that as a consequence of considering a generalized statistics, an effective interaction arises but the interaction is not enough to generate a phase transition. This generalized entropy seems to be relevant in confinement or in systems with not so many degrees of freedom, so it could be interesting to use such entropies to characterize the thermodynamics of small systems.

Making thermodynamic functions of nanosystems intensive

International Nuclear Information System (INIS)

Nassimi, A M; Parsafar, G A

2007-01-01

The potential energy of interaction among particles in many systems is proportional to r -α . In systems for which α< d, we encounter nonextensive (nonintensive) thermodynamic functions, where d is the space dimension. A scaling parameter, N-tilde, has been introduced to make the nonextensive (nonintensive) thermodynamic functions of such systems extensive (intensive). Our simulation results show that this parameter is not capable of making the thermodynamic functions of a nanosystem extensive (intensive). Here we have presented a theoretical justification for N-tilde. Then we have generalized this scaling parameter to be capable of making the nonextensive (nonintensive) thermodynamic functions of nanosystems extensive (intensive). This generalized parameter is proportional to the potential energy per particle at zero temperature

Statistical learning and prejudice.

Science.gov (United States)

Madison, Guy; Ullén, Fredrik

2012-12-01

Human behavior is guided by evolutionarily shaped brain mechanisms that make statistical predictions based on limited information. Such mechanisms are important for facilitating interpersonal relationships, avoiding dangers, and seizing opportunities in social interaction. We thus suggest that it is essential for analyses of prejudice and prejudice reduction to take the predictive accuracy and adaptivity of the studied prejudices into account.

A statistical design of experiments for optimizing the MALDI-TOF-MS sample preparation of polymers. An application in the assessment of the thermo-mechanical degradation mechanisms of poly (ethylene terephthalate)

International Nuclear Information System (INIS)

Badia, J.D.; Stroemberg, E.; Ribes-Greus, A.; Karlsson, S.

2011-01-01

The sample preparation procedure for MALDI-TOF MS of polymers is addressed in this study by the application of a statistical Design of Experiments (DoE). Industrial poly (ethylene terephthalate) (PET) was chosen as model polymer. Different experimental settings (levels) for matrixes, analyte/matrix proportions and concentrations of cationization agent were considered. The quality parameters used for the analysis were signal-to-noise ratio and resolution. A closer inspection of the statistical results provided the study not only with the best combination of factors for the MALDI sample preparation, but also with a better understanding of the influence of the different factors, individually or in combination, to the signal. The application of DoE for the improvement of the MALDI measure of PET stated that the best combination of factors and levels was the following: matrix (dithranol), proportion analyte/matrix/cationization agent (1/15/1, V/V/V), and concentration of cationization agent (2 g L -1 ). In a second part, multiple processing by means of successive injection cycles was used to simulate the thermo-mechanical degradation effects on the oligomeric distribution of PET under mechanical recycling. The application of MALDI-TOF-MS showed that thermo-mechanical degradation primarily affected initially predominant cyclic species. Several degradation mechanisms were proposed, remarking intramolecular transesterification and hydrolysis. The ether links of the glycol unit in PET were shown to act as potential reaction sites, driving the main reactions of degradation.

Investigation of thermodynamic and mechanical properties of AlyIn1-yP alloys by statistical moment method

Science.gov (United States)

Ha, Vu Thi Thanh; Hung, Vu Van; Hanh, Pham Thi Minh; Tuyen, Nguyen Viet; Hai, Tran Thi; Hieu, Ho Khac

2018-03-01

The thermodynamic and mechanical properties of III-V zinc-blende AlP, InP semiconductors and their alloys have been studied in detail from statistical moment method taking into account the anharmonicity effects of the lattice vibrations. The nearest neighbor distance, thermal expansion coefficient, bulk moduli, specific heats at the constant volume and constant pressure of the zincblende AlP, InP and AlyIn1-yP alloys are calculated as functions of the temperature. The statistical moment method calculations are performed by using the many-body Stillinger-Weber potential. The concentration dependences of the thermodynamic quantities of zinc-blende AlyIn1-yP crystals have also been discussed and compared with those of the experimental results. Our results are reasonable agreement with earlier density functional theory calculations and can provide useful qualitative information for future experiments. The moment method then can be developed extensively for studying the atomistic structure and thermodynamic properties of nanoscale materials as well.

On application of non—extensive statistical mechanics to studying ecological diversity

International Nuclear Information System (INIS)

Van Xuan, Le; Lan, Nguyen Tri; Viet, Nguyen Ai

2016-01-01

The concept of Tsallis entropy provides an extension of thermodynamics and statistical physics. In the ecology, Tsallis entropy is proposed to be a new class of diversity indices S_q which covers many common diversity indices found in ecological literature. As a new statistical model for the Whittaker plots describing species abundance distribution, the truncated exponential distribution is used to calculate the diversity and evenness indices. The obtained results in new model are graphically compared with those in previous publication in the same field of interests, and shows a good agreement. A further development of a thermodynamic theory of ecological systems that is consistent with entropic approach of statistical physics is motivated. (paper)

Fracture mechanics and statistical modeling of ternary blends of polylactide/ethylene-acrylate copolymer /wood-flour composites

Science.gov (United States)

Afrifah, Kojo Agyapong

This study examined the mechanisms of toughening the brittle bio-based poly(lactic acid) (PLA) with a biodegradable rubbery impact modifier to develop biodegradable and cost effective PLA/wood-flour composites with improved impact strength, toughness, high ductility, and flexibility. Semicrystalline and amorphous PLA grades were impact modified by melt blending with an ethylene-acrylate copolymer (EAC) impact modifier. EAC content was varied to study the effectiveness and efficiency of the impact modifier in toughening the semicrystalline and amorphous grades of the PLA. Impact strength was used to assess the effectiveness and efficiency of the EAC in toughening the blends, whereas the toughening mechanisms were determined with the phase morphologies and the miscibilities of the blends. Subsequent tensile property analyses were performed on the most efficiently toughened PLA grade. Composites were made from PLA, wood flour of various particle sizes, and EAC. Using two-level factorial design the interaction between wood flour content, wood flour particle size, and EAC content and its effect on the mechanical properties of the PLA/wood-flour composites was statistically studied. Numerical optimization was also performed to statistically model and optimize material compositions to attain mechanical properties for the PLA/wood-flour composites equivalent to at least those of unfilled PLA. The J-integral method of fracture mechanics was applied to assess the crack initiation (Jin) and complete fracture (J f) energies of the composites to account for imperfections in the composites and generate data useful for engineering designs. Morphologies of the fractured surfaces of the composites were analyzed to elucidate the failure and toughening mechanisms of the composites. The EAC impact modifier effectively improved the impact strength of the PLA/EAC blends, regardless of the PLA type. However, the EAC was more efficient in the semicrystalline grades of PLA compared to the

A Statistical Mechanics Approach to Approximate Analytical Bootstrap Averages

DEFF Research Database (Denmark)

Malzahn, Dorthe; Opper, Manfred

2003-01-01

We apply the replica method of Statistical Physics combined with a variational method to the approximate analytical computation of bootstrap averages for estimating the generalization error. We demonstrate our approach on regression with Gaussian processes and compare our results with averages...

Erwin Schroedinger: Collected papers V. 1. Contributions to statistical mechanics

International Nuclear Information System (INIS)

Schroedinger, E.

1984-01-01

38 publications reprinted in this volume show that the interest for statistical problems accompanied Schroedinger during his entire scientific career. Already in his second paper he worked on the magnetism of solid states. The classical considerations come close to the heart of diamagnetism and also to the origin of paramagnetism. In classical investigations of the specific heat Schroedinger helped through abstract theory but also by analysing a gigantic amount of experimental material. In 1926 he and F. Kohlrausch actually played the 'Urngame of Ehrenfest' as a model of the H-curve and published the results. Inclination towards experimenting, sequences of measurements and statistical evaluation of experimental data led to papers on the foundation of the theory of probability, where he tries to put the subjective probability concept on into a systematic framework. Two earlier papers on dynamics of the elastic chain remained particularly valuable. By solving the initial value problem with Bessel-functions this many-body-problem is led to an explicit discussion. These studies are likely to be the roots of another keynote in Schroedinger's thinking, namely, the irreversibility. 1945 a statistical theory of chain-reactions was published under the inconspicuous title of 'Probability Problems in Nuclear Chemistry'. In his last work Schroedinger turns off in a wrong direction: it is that energy should only be a statistical concept and should not be conserved in elementary processes, but somehow only in the mean. These short remarks only illuminate the diversity of the material in this volume, but testify Schroedinger's deep understanding in this field. (W.K.)

Conceptual developments of non-equilibrium statistical mechanics in the early days of Japan

Science.gov (United States)

Ichiyanagi, Masakazu

1995-11-01

This paper reviews the research in nonequilibrium statistical mechanics made in Japan in the period between 1930 and 1960. Nearly thirty years have passed since the discovery of the exact formula for the electrical conductivity. With the rise of the linear response theory, the methods and results of which are quickly grasped by anyone, its rationale was pushed aside and even at the stage where the formulation was still incomplete some authors hurried to make physical applications. Such an attitude robbed it of most of its interest for the average physicist, who would approach an understanding of some basic concept, not through abstract and logical analysis but by simply increasing his technical experiences with the concept. The purpose of this review is to rescue the linear response theory from being labeled a mathematical tool and to show that it has considerable physical content. Many key papers, originally written in Japanese, are reproduced.