Concavity, Response Functions and Replica Energy

TL;DR

This paper explores how negative response functions and ensemble inequivalence in nonadditive systems relate to the concavity of thermodynamic potentials, emphasizing the role of the replica energy in such systems.

Contribution

It analyzes the dependence of negative response functions on which thermodynamic quantities are constrained and highlights the significance of the replica energy in nonadditive systems.

Findings

Negative response functions depend on constraints on E, V, N.

Unconstrained ensemble involves the replica energy, relevant for nonadditive systems.

Replica energy vanishes in additive systems, indicating its importance in nonadditive thermodynamics.

Abstract

In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated to the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are constrained in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, physically meaningful only for nonadditive systems. In fact, its partition function is associated to the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems.