Concavity, response functions and replica energy

Alessandro Campa, Lapo Casetti, Ivan Latella, Agustín Pérez-Madrid, Stefano Ruffo

Research output: Contribution to journalArticlepeer-review


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 with 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, which is physically meaningful only for nonadditive systems. In fact, its partition function is associated with the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems.

Original languageEnglish
Article number907
Issue number12
Publication statusPublished - Dec 1 2018


  • Ensemble inequivalence
  • Long-range interactions
  • Non-additive systems
  • Computational Physics

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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