Equilibrium fluctuation theorems compatible with anomalous response

Abstract

Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations $C={\beta }^2<\delta U^2>$, which is able to describe the existence of macrostates with negative heat capacities $C<0$. In this work, we extend our previous results for an equilibrium situation with several control parameters to account for the existence of states with anomalous values in other response functions. Our analysis leads to the derivation of three different equilibrium fluctuation theorems: the \textit{fundamental and the complementary fluctuation theorems}, which represent the generalization of two fluctuation identities already obtained in previous works, and the \textit{associated fluctuation theorem}, a result that has no counterpart in the framework of Boltzmann-Gibbs distributions. These results are applied to study the anomalous susceptibility of a ferromagnetic system, in particular, the case of 2D Ising model.

Extended version of the paper published in JSTAT

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Cited by in corpus (5)

• Curvature of fluctuation geometry and its implications on Riemannian fluctuation theory
• Improving the efficiency of Monte Carlo simulations of systems that undergo temperature-driven phase transitions
• Extended canonical Monte Carlo methods: Improving accuracy of microcanonical calculations using a re-weighting technique
• Understanding critical behavior in the framework of the extended equilibrium fluctuation theorem
• Fluctuation geometry: A counterpart approach of inference geometry