Abstract
We show that the configurational probability distribution of a classical gas always belongs to the q-exponential family. One of the consequences of this observation is that the thermodynamics of the configurational subsystem is uniquely determined up to a scaling function. As an example we consider a system of non-interacting harmonic oscillators. In this example, the scaling function can be determined from the requirement that in the limit of large systems the microcanonical temperature of the configurational subsystem should coincide with that of the canonical ensemble. The result suggests that R´enyi’s entropy function is the relevant one rather than that of Tsallis.
Highlights
Many-particle systems are usually studied in the canonical or grandcanonical ensemble
We show that the configurational probability distribution of a classical gas always belongs to the q-exponential family
The main purpose of the present paper is to point out that the configurational probability distribution of a classical gas always belongs to the q-exponential family
Summary
Many-particle systems are usually studied in the canonical or grandcanonical ensemble. One concludes from (16) that the configurational density function fUconf (q) of a classical gas in the microcanonical ensemble with parameter U always belongs to the q-exponential family with the constant q given by (17). It is well-known that the q-exponential distribution optimizes the Tsallis entropy [20] and that together with the configurational energy U conf it satisfies the thermodynamic duality relations [10].
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