Concavity, Response Functions and Replica Energy

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.

22 pages, 2 figures

References in corpus (6)

• The large deviation approach to statistical mechanics
• Statistical mechanics and dynamics of solvable models with long-range interactions
• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Partial equivalence of statistical ensembles and kinetic energy
• Long-range interacting systems in the unconstrained ensemble
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Cited by in corpus (7)

• $\mu PT$ statistical ensemble: systems with fluctuating energy, particle number, and volume
• Phase transitions in the unconstrained ensemble
• Quantum thermochemical engines
• Lifetime of locally stable states near a phase transition in the Thirring model
• Modified Thirring model beyond the excluded-volume approximation
• Monte Carlo Simulations of Crystal Defects in Open Ensembles
• A condensed-matter analogue of the false vacuum