Statistical Physics Is More than Statistical Mechanics

2012 ◽  
pp. 1-2
Author(s):  
Josef Honerkamp
Keyword(s):  
Statistical Mechanics ◽  
Statistical Physics

Chapter 22. Connections to Statistical Physics

2021 ◽  
Author(s):  
Fabrizio Altarelli ◽  
Rémi Monasson ◽  
Guilhem Semerjian ◽  
Francesco Zamponi
Keyword(s):  
Phase Transitions ◽  
Low Temperature ◽  
Statistical Mechanics ◽  
Cost Function ◽  
Computer Science ◽  
Statistical Physics ◽  
Energy Landscape ◽  
Research Activity ◽  
Detailed Picture ◽  
Intense Research

This chapter surveys a part of the intense research activity that has been devoted by theoretical physicists to the study of randomly generated k-SAT instances. It can be at first sight surprising that there is a connection between physics and computer science. However low-temperature statistical mechanics concerns precisely the behaviour of the low-lying configurations of an energy landscape, in other words the optimization of a cost function. Moreover the ensemble of random k-SAT instances exhibit phase transitions, a phenomenon mostly studied in physics (think for instance at the transition between liquid and gaseous water). Besides the introduction of general concepts of statistical mechanics and their translations in computer science language, the chapter presents results on the location of the satisfiability transition, the detailed picture of the satisfiable regime and the various phase transitions it undergoes, and algorithmic issues for random k-SAT instances.

scholarly journals Landau's statistical mechanics for quasi-particle models

2014 ◽  
Vol 29 (10) ◽  
pp. 1450056 ◽  
Author(s):  
Vishnu M. Bannur
Keyword(s):  
Energy Density ◽  
Statistical Mechanics ◽  
Quark Gluon Plasma ◽  
Statistical Physics ◽  
Particle System ◽  
Gluon Plasma ◽  
Particle Model ◽  
Quasi Particle ◽  
Thermodynamics And Statistical Mechanics

Landau's formalism of statistical mechanics [following L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon Press, Oxford, 1980)] is applied to the quasi-particle model of quark–gluon plasma. Here, one starts from the expression for pressure and develop all thermodynamics. It is a general formalism and consistent with our earlier studies [V. M. Bannur, Phys. Lett. B647, 271 (2007)] based on Pathria's formalism [following R. K. Pathria, Statistical Mechanics (Butterworth-Heinemann, Oxford, 1977)]. In Pathria's formalism, one starts from the expression for energy density and develop thermodynamics. Both the formalisms are consistent with thermodynamics and statistical mechanics. Under certain conditions, which are wrongly called thermodynamic consistent relation, we recover other formalism of quasi-particle system, like in M. I. Gorenstein and S. N. Yang, Phys. Rev. D52, 5206 (1995), widely studied in quark–gluon plasma.

The Emergence of Statistical Mechanics

2017 ◽  
Author(s):  
Olivier Darrigol ◽  
Jürgen Renn
Keyword(s):  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Statistical Physics ◽  
Second Law Of Thermodynamics ◽  
Boltzmann Distribution ◽  
Probabilistic Interpretation ◽  
Specific Heats ◽  
Mechanical Models ◽  
History Of ◽  
Thermal Phenomena

This article traces the history of statistical mechanics, beginning with a discussion of mechanical models of thermal phenomena. In particular, it considers how several circumstances, including the establishment of thermodynamics in the mid-nineteenth century, led to a focus on the model of heat as a motion of particles. It then describes the concept of heat as fluid and the kinetic theory before turning to gas theory and how it served as a bridge between mechanics and thermodynamics. It also explores gases as particles in motion, the Maxwell–Boltzmann distribution, the problem of specific heats, challenges to the second law of thermodynamics, and the probabilistic interpretation of entropy. Finally, it examines how the results of the kinetic theory assumed a new meaning as cornerstones of a more broadly conceived statistical physics, along with Josiah Willard Gibbs and Albert Einstein’s development of statistical mechanics as a synthetic framework.

scholarly journals THERMODYNAMIC LIMIT IN STATISTICAL PHYSICS

2014 ◽  
Vol 28 (09) ◽  
pp. 1430004 ◽  
Author(s):  
A. L. KUZEMSKY
Keyword(s):  
Statistical Mechanics ◽  
Thermodynamic Limit ◽  
Statistical Physics ◽  
Formal Series ◽  
Distribution Functions ◽  
Particle Systems ◽  
Boltzmann Equations ◽  
Qualitative Understanding ◽  
Statistical Ensembles ◽  
Equipartition Of Energy

The thermodynamic limit in statistical thermodynamics of many-particle systems is an important but often overlooked issue in the various applied studies of condensed matter physics. To settle this issue, we review tersely the past and present disposition of thermodynamic limiting procedure in the structure of the contemporary statistical mechanics and our current understanding of this problem. We pick out the ingenious approach by Bogoliubov, who developed a general formalism for establishing the limiting distribution functions in the form of formal series in powers of the density. In that study, he outlined the method of justification of the thermodynamic limit when he derived the generalized Boltzmann equations. To enrich and to weave our discussion, we take this opportunity to give a brief survey of the closely related problems, such as the equipartition of energy and the equivalence and nonequivalence of statistical ensembles. The validity of the equipartition of energy permits one to decide what are the boundaries of applicability of statistical mechanics. The major aim of this work is to provide a better qualitative understanding of the physical significance of the thermodynamic limit in modern statistical physics of the infinite and "small" many-particle systems.

scholarly journals The maximum entropy production principle: two basic questions

2010 ◽  
Vol 365 (1545) ◽  
pp. 1333-1334 ◽  
Author(s):  
Leonid M. Martyushev
Keyword(s):  
Statistical Mechanics ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Statistical Physics ◽  
Overwhelming Majority ◽  
Equilibrium Thermodynamics ◽  
Maximum Entropy Production ◽  
Environmental Systems ◽  
Thermodynamics And Statistical Mechanics ◽  
Non Equilibrium

The overwhelming majority of maximum entropy production applications to ecological and environmental systems are based on thermodynamics and statistical physics. Here, we discuss briefly maximum entropy production principle and raises two questions: (i) can this principle be used as the basis for non-equilibrium thermodynamics and statistical mechanics and (ii) is it possible to ‘prove’ the principle? We adduce one more proof which is most concise today.

A non-extensive statistical physics view in Earth Physics: Geodynamic properties in terms of Complexity theory .

2020 ◽  
Author(s):  
Filippos Vallianatos
Keyword(s):  
Statistical Mechanics ◽  
Gaussian Distribution ◽  
Plate Tectonics ◽  
Statistical Physics ◽  
Extreme Values ◽  
Global Scale ◽  
Coda Wave ◽  
Research And Innovation ◽  
Classical Thermodynamics ◽  
Earth Dynamics

<p>Boltzmann-Gibbs (BG) statistical physics is one of the cornerstones of contemporary physics. It establishes a remarkably useful bridge between the mechanical microscopic laws and macroscopic description using classical thermodynamics. If long-range interactions, non-markovian microscopic memory, multifractal boundary conditions and multifractal structures are present then another type of statistical mechanics, than BG, seems appropriate to describe nature (Tsallis, 2001).</p><p>To overcome at least some of these anomalies that seem to violate BG statistical mechanics, non-extensive statistical physics (NESP) was proposed by Tsallis  (Tsallis, 1988) that recovers the extensive BG as a particular case. The associated generalized entropic form controlled by the entropic index  q that represents a measure of non-additivity of a system. S<sub>q</sub> recovers S<sub>BG</sub> in the limit q→1. For a variable X with a probability distribution p(X), as that of seismic moment , inter-event times  or distances between the successive earthquakes or the length of faults in a given region, using terms of NESP, we obtain the physical probability which expressed by a q-exponential function as defined in Tsallis, (2009).  Another type of distributions that are deeply connected to statistical physics is that of the squared variable X<sup>2</sup>. In BG statistical physics, the distribution of X<sup>2</sup> corresponds to the well-known Gaussian distribution. If we optimize S<sub>q</sub> for X<sup>2</sup>, we obtain a generalization of the normal Gaussian that is known as q-Gaussian distribution (Tsallis, 2009). In the limit q→1, the normal Gaussian distribution, recovered. For q> 1, the q-Gaussian distribution has power-law tails with slope -2/(q-1), thus enhancing the probability of the extreme values.</p><p>In the present work we review a collection of Earth physics problems such as a) NESP pathways in earthquake size distribution, b) The effect of mega-earthquakes, c) Spatiotemporal description of Seismicity, d) the plate tectonics as a case of non-extensive thermodynamics e) laboratory seismology and fracture, f) the non-extensive nature of earth’s ambient noise, and g) evidence of non-extensivity in eartquakes’ coda wave. The aforementioned cases cover the most of the problems in Earth Physics indicated that non extensive statistical physics could be the underline interpretation tool to understand earth's evolution and dynamics.</p><p>We can state that the study of the non-extensive statistical physics of earth dynamics remains wide-open with many significant discoveries to be made. The results of the analysis in the cases described previously indicate that the ideas of NESP can be used to express the non-linear dynamics that control the evolution of the earth dynamics at different scales. The key scientific challenge is to understand in a unified way, using NESP principles, the physical mechanisms that drive the evolution of fractures ensembles in laboratory and global scale and how we can use measures of evolution that will forecast the extreme fracture event rigorously and with consistency.</p><p><strong> </strong><strong>Acknowledgments. </strong>We acknowledge support by the project “HELPOS – Hellenic System for Lithosphere Monitoring” (MIS 5002697) which is implemented under the Action “Reinforcement of the Research and Innovation Infrastructure”, funded by the Operational Programme "Competitiveness, Entrepreneurship and Innovation" (NSRF 2014-2020) and co-financed by Greece & European Union (ERDF).</p><p><strong> </strong></p>

scholarly journals On Quantum Statistical Mechanics: A Study Guide

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Wladyslaw Adam Majewski
Keyword(s):  
Statistical Mechanics ◽  
Statistical Physics ◽  
Algebraic Approach ◽  
Quantum Statistical Mechanics ◽  
Quantum Correlations ◽  
New Formalism ◽  
Mathematical Structures ◽  
Infinite Dimensional ◽  
Quantum Statistical ◽  
Large Quantum

We provide an introduction to a study of applications of noncommutative calculus to quantum statistical physics. Centered on noncommutative calculus, we describe the physical concepts and mathematical structures appearing in the analysis of large quantum systems and their consequences. These include the emergence of algebraic approach and the necessity of employment of infinite-dimensional structures. As an illustration, a quantization of stochastic processes, new formalism for statistical mechanics, quantum field theory, and quantum correlations are discussed.

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