Ideal gas provides q-entropy

TL;DR

This paper introduces a mathematical method to derive deformed entropy formulas, such as Renyi and Tsallis, for finite systems like an ideal gas, revealing new dualities and generalized entropy expressions.

Contribution

It presents a novel procedure to obtain deformed entropy formulas based on zero mutual information, and introduces a new generalized entropy formula for systems with linear heat capacity relations.

Findings

Derivation of Renyi and Tsallis entropy formulas for ideal gases.

Identification of a q*-duality from different statistical approaches.

Construction of a new generalized deformed entropy formula.

Abstract

A mathematical procedure is suggested to obtain deformed entropy formulas of type K(S_K) = sum_i P_i K(-ln P_i), by requiring zero mutual K(S_K)-information between a finite subsystem and a finite reservoir. The use of this method is first demonstrated on the ideal gas equation of state with finite constant heat capacity, C, where it delivers the Renyi and Tsallis formulas. A novel interpretation of the qstar = 2-q duality arises from the comparison of canonical subsystem and total microcanonical partition approaches. Finally a new, generalized deformed entropy formula is constructed for the linear relation C(S) = C_0 + C_1 S.