Skip to main content
Select Source:

statistical mechanics

statistical mechanics, quantitative study of systems consisting of a large number of interacting elements, such as the atoms or molecules of a solid, liquid, or gas, or the individual quanta of light (see photon) making up electromagnetic radiation. Although the nature of each individual element of a system and the interactions between any pair of elements may both be well understood, the large number of elements and possible interactions can present an almost overwhelming challenge to the investigator who seeks to understand the behavior of the system. Statistical mechanics provides a mathematical framework upon which such an understanding may be built. Since many systems in nature contain large number of elements, the applicability of statistical mechanics is broad. In contrast to thermodynamics, which approaches such systems from a macroscopic, or large-scale, point of view, statistical mechanics usually approaches systems from a microscopic, or atomic-scale, point of view. The foundations of statistical mechanics can be traced to the 19th-century work of Ludwig Boltzmann, and the theory was further developed in the early 20th cent. by J. W. Gibbs. In its modern form, statistical mechanics recognizes three broad types of systems: those that obey Maxwell-Boltzmann statistics, those that obey Bose-Einstein statistics, and those that obey Fermi-Dirac statistics. Maxwell-Boltzmann statistics apply to systems of classical particles, such as the atmosphere, in which considerations from the quantum theory are small enough that they may be ignored. The other two types of statistics concern quantum systems: systems in which quantum-mechanical properties cannot be ignored. Bose-Einstein statistics apply to systems of bosons (particles that have integral values of the quantum mechanical property called spin); an unlimited number of bosons can be placed in the same state. Photons, for instance, are bosons, and so the study of electromagnetic radiation, such as the radiation of a blackbody involves the use of Bose-Einstein statistics. Fermi-Dirac statistics apply to systems of fermions (particles that have half-integral values of spin); no two fermions can exist in the same state. Electrons are fermions, and so Fermi-Dirac statistics must be employed for a full understanding of the conduction of electrons in metals. Statistical mechanics has also yielded deep insights in the understanding of magnetism, phase transitions, and superconductivity.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"statistical mechanics." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 24 Apr. 2018 <http://www.encyclopedia.com>.

"statistical mechanics." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (April 24, 2018). http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/statistical-mechanics

"statistical mechanics." The Columbia Encyclopedia, 6th ed.. . Retrieved April 24, 2018 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/statistical-mechanics

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.

statistical mechanics

statistical mechanics Branch of physics that studies large-scale properties of matter based on the statistical laws of large numbers. The large number of molecules in such a system allows the use of statistics to predict the probability of finding the system in any state. The entropy (disorder or randomness) of the system relates to its number of possible states; a system left to itself will tend to approach the most probable distribution of energy states. See also thermodynamics

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"statistical mechanics." World Encyclopedia. . Encyclopedia.com. 24 Apr. 2018 <http://www.encyclopedia.com>.

"statistical mechanics." World Encyclopedia. . Encyclopedia.com. (April 24, 2018). http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/statistical-mechanics

"statistical mechanics." World Encyclopedia. . Retrieved April 24, 2018 from Encyclopedia.com: http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/statistical-mechanics

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.