World Library  
Flag as Inappropriate
Email this Article

Statistical physics

Article Id: WHEBN0000029518
Reproduction Date:

Title: Statistical physics  
Author: World Heritage Encyclopedia
Language: English
Subject: Kinetic exchange models of markets, H. Eugene Stanley, Statistical mechanics, Michael Fisher, Combinatorics and physics
Publisher: World Heritage Encyclopedia

Statistical physics

Statistical physics is a branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, neurology, and even some social sciences, such as sociology. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.[1]

In particular, statistical mechanics develops the phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.

Statistical mechanics

Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics, classical mechanics, and quantum mechanics at the microscopic level. Because of this history, the statistical physics is often considered synonymous with statistical mechanics or statistical thermodynamics.[note 1]

One of the most important equations in Statistical mechanics (analogous to F=ma in mechanics, or the Schrödinger equation in quantum mechanics ) is the definition of the partition function Z, which is essentially a weighted sum of all possible states q available to a system.

Z = \sum_q \mathrm{e}^{-\frac{E(q)}{k_BT}}

where k_B is the Boltzmann constant, T is temperature and E(q) is energy of state q. Furthermore, the probability of a given state, q, occurring is given by

P(q) = \frac{ {\mathrm{e}^{-\frac{E(q)}{k_BT}}}}{Z}

Here we see that very-high-energy states have little probability of occurring, a result that is consistent with intuition.

A statistical approach can work well in classical systems when the number of degrees of freedom (and so the number of variables) is so large that exact solution is not possible, or not really useful. Statistical mechanics can also describe work in non-linear dynamics, chaos theory, thermal physics, fluid dynamics (particularly at high Knudsen numbers), or plasma physics.

Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes the large processing power of modern computers to simulate or approximate solutions. A common approach to statistical problems is to use a Monte Carlo simulation to yield insight into the dynamics of a complex system.

See also


  1. ^ This article presents a broader sense of the definition of statistical physics


  1. ^ Huang, Kerson. Introduction to Statistical Physics (2nd ed.). CRC Press. p. 15.  


Thermal and Statistical Physics (lecture notes, Web draft 2001) by Mallett M., Blumler P.

BASICS OF STATISTICAL PHYSICS: Second Edition by Harald J W Müller-Kirsten (University of Kaiserslautern, Germany)

Statistical physics by Kadanoff L.P.

Statistical Physics - Statics, Dynamics and Renormalization by Kadanoff L.P.

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.