|
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 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 black body
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.
|