Additive entropy underlying the general composable entropy prescribed by thermodynamic meta-equilibrium

TL;DR

This paper derives an additive entropy form underlying a general composable entropy in thermodynamic meta-equilibrium, connecting Tsallis-type nonadditivity with a monotonic transformation.

Contribution

It introduces a method to identify the additive entropy underlying a broad class of composable entropies in thermodynamics.

Findings

Derived the additive entropy from composable entropy using common intensive variables.

Showed that the simplest composable entropy satisfies Tsallis-type nonadditivity.

Established that meta-equilibrium can be described by the maximum of a monotonic function of the entropy.

Abstract

We consider the meta-equilibrium state of a composite system made up of independent subsystems satisfying the additive form of external constraints, as recently discussed by Abe [Phys. Rev. E {\bf 63}, 061105 (2001)]. We derive the additive entropy $S$ underlying a composable entropy $\tilde{S}$ by identifying the common intensive variable. The simplest form of composable entropy satisfies Tsallis-type nonadditivity and the most general composable form is interpreted as a monotonically increasing funtion $H$ of this simplest form. This is consistent with the observation that the meta-equilibrium can be equivalently described by the maximum of either $H[\tilde{S}]$ or $\tilde{S}$ and the intensive variable is same in both cases.