The dual formalisms of nonextensive thermodynamics for open systems with maximum entropy principle

Abstract

We study the nonextensive thermodynamics for open systems. On the basis of the maximum entropy principle, the dual power-law q-distribution functions are re-deduced by using the dual particle number definitions and assuming that the chemical potential is constant in the two sets of parallel formalisms, where the fundamental thermodynamic equations with dual interpretations of thermodynamic quantities are derived for the open systems. By introducing parallel structures of Legendre transformations, other thermodynamic equations with dual interpretations of quantities are also deduced in the open systems, and then several dual thermodynamic relations are inferred. One can easily find that there are correlations between the dual relations, from which an equivalent rule is found that the Tsallis factor is invariable in calculations of partial derivative with constant volume or constant entropy. Using this rule, more correlations can be found. And the statistical expressions of the Lagrange internal energy and pressure are easily obtained.

Thermodynamic properties of the solid and metal electrons in the nonextensive quantum statistics with a nonextensive parameter transformation

“…( 23) respectively. Such a parameter transformation also introduces a generalized Nature Index in the form of ( 31) and thus we produce a generalized Debye model (41) in the nonextensive quantum statistics. These new expressions all depend significantly on the nonextensive parameter ν and when we take ν→1, they all recover to the forms in the classical quantum statistics.…”

“…It can be seen that at a room temperature, the thermal motion energy kT (the temperature T is identical to the thermodynamic temperature in the classical statistics [41]) is very small relative to the chemical μ. Therefore, the correction effect caused by the Tsallis factor is very small and can be ignored, so indicating that c q =1.…”

“…This definition approach is of the third choice of internal energy definition [40], from which one can find that the particle number and internal energy are both additive. This energy is called Lagrange internal energy [39,41]. Similarly, the particle number is called the Lagrange particle number.…”