## statistical mechanics

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## Statistical Mechanics

# Statistical Mechanics

Statistical mechanics is a sub-branch of physics that attempts to predict and explain the behavior of a macroscopic system based on the behavior and properties of that system’s microscopic elements. It uses the principles of statistics and probability, found within mathematics, to describe particles (microscopic elements) acted on by forces, thus, implying motions.

The number of these microscopic elements is usually very large, and it is impossible to accurately predict the behavior of each of these elements as they interact. However, the large number of interactions makes it theoretically possible for statistical mechanics to predict the behavior of the system as a whole.

Scottish-English physicist James Clerk Maxwell (1831–1879), Italian mathematician and physicist Ludwig Boltzmann (1844–1906), and American mathematical physicist Josiah Willard Gibbs (1839–1903) are considered the first scientists to have developed the concepts within statistical mechanics. Each physicist conjectured that matter was composed of very small particles that were always in motion. They were unable to deal with these atoms and molecules individually so decided to group them together. They averaged the dynamic microscopic properties of the individual particles with statistical techniques; thus, developing a macroscopic measure of the group’s thermodynamic characteristics. Consequently, statistical mechanics was able to explain thermodynamics with the use of statistics and mechanics.

Later, in the early part of the twentieth century, statistical mechanics incorporated quantum theory when German physicist Maxwell Planck (1858–1947) proposed that atoms absorb or emit electromagnetic radiation in bundles of energy termed “quanta.” Later, physicists Niels Bohr (1885–1962), J.J. Thomson (1856–1940), and Ernest Rutherford (1871–1937) studied Planck’s quantum theory of radiation and improved on Planck’s quantum theory.

Today, statistical mechanics uses the Maxwell-Boltzmann statistics to describe the behavior of a group of classical particles. When describing quantum particles (fermions and bosons), statistical mechanics uses Fermi-Dirac statistics, when working with fermions, and Bose-Einstein statistics, when operating with bosons. Scientists apply the spectroscopic data of individual molecules when calculating, with the use of statistical mechanics, the thermodynamic properties of materials.

## 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.

## 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

## Statistical Mechanics

# Statistical mechanics

Statistical mechanics is a sub-branch of **physics** that attempts to explain the behavior of a macroscopic system based on the behavior and properties of that system's microscopic elements.

The number of these microscopic elements is usually very large, and it is impossible to accurately predict the behavior of each of these elements as they interact. However, the large number of interactions makes it theoretically possible for statistical mechanics to predict the behavior of the system as a whole.