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Thermodynamic betaIn statistical mechanics, the thermodynamic beta is a numerical quantity related to the thermodynamic temperature of a system. The thermodynamic beta can be viewed as a connection between the statistical interpretation of a physical system and thermodynamics. Additional recommended knowledge
DetailsStatistical interpretationFrom the statistical point of view, β is a numerical quantity relating two macroscopic systems in equilibrium. The exact formulation is as follows. Consider two systems, 1 and 2, in thermal contact, with respective energies E_{1} and E_{2}. We assume E_{1} + E_{2} = some constant E. The number of microstates of each system will be denoted by Ω_{1} and Ω_{2}. Under our assumptions Ω_{i} depends only on E_{i}. Thus the number of microstates for the combined system is We will derive β from the following fundamental assumption:
(In other words, the system naturally seeks the maximum number of microstates.) Therefore, at equilibrium, But E_{1} + E_{2} = E implies So i.e. The above relation motivates the definition of β: Connection with thermodynamic viewOn the other hand, when two systems are in equilibrium, they have the same thermodynamic temperature T. Thus intuitively one would expect that β be related to T in some way. This link is provided by the formula where k is the Boltzmann constant. So Substituting into the definition of β gives Comparing with the thermodynamic formula we have where τ is sometimes called the fundamental temperature of the system with units of energy. See alsoCategories: Thermodynamics  Units of temperature 

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Thermodynamic_beta". A list of authors is available in Wikipedia. 