Statistical weight is a physical quantity that determines in quantum mechanics and quantum statistics the number of different quantum states of a system with the same energy (synonym: multiplicity of degeneracy of the energy level ). In statistical physics and thermodynamics, the statistical weight is the number of methods (microstates of a system) by which this macroscopic state of a statistical system can be realized. Statistical weight is usually denoted by Γ, g , w , W, or Ω .
By the above definition, a statistical weight is a dimensionless integer greater than or equal to one, . Sometimes statistical weight is called thermodynamic probability , although it should be noted that probability is usually defined as a real number in the range from 0 to 1.
When considering quantum systems with a continuous energy spectrum, statistical weight is usually understood as the number of quantum states falling within a certain energy interval. In this definition, the statistical weight has the dimension of reverse energy.
In the semiclassical approximation, the measure of the statistical weight is the phase volume of the system, which falls on a certain energy interval. If the system has n degrees of freedom , then the phase volume and the corresponding statistical weight are expressed in units of h n , where h is the Planck constant .
The entropy S of the system and its statistical weight are related by the Boltzmann relation : S = k ln w (here k is the Boltzmann constant ).
The statistical weight determined in terms of the phase volume or the number of microstates is a multiplicative physical quantity: if the system consists of two non-interacting subsystems with statistical weights w 1 and w 2 , then the total statistical weight of the system is W = w 1 w 2 .
See also
- Statistical amount
Literature
- Physical Encyclopedia. In 5 volumes. - M .: Soviet Encyclopedia. Editor-in-chief A.M. Prokhorov. 1988.
- Degeneracy . In: IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by AD McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8 . doi: 10.1351 / goldbook.