# Equilibrium fluctuation theorems compatible with anomalous response

## TL;DR

This paper generalizes fluctuation theorems to describe anomalous response functions in equilibrium systems, including negative heat capacities and susceptibilities, with applications to models like the 2D Ising system.

## Contribution

It introduces three new equilibrium fluctuation theorems that extend previous identities to account for anomalous response functions in complex systems.

## Key findings

- Derived three new fluctuation theorems for anomalous responses.
- Applied the theorems to the 2D Ising model's susceptibility.
- Demonstrated the existence of states with negative heat capacity.

## 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.