Understanding critical behavior in the framework of the extended equilibrium fluctuation theorem

TL;DR

This paper extends the equilibrium fluctuation theorem to systems with anomalous responses, revealing how environmental influences can alter critical phenomena and the divergence of correlation lengths.

Contribution

It introduces a new fluctuation theorem that explains the environmental impact on critical behavior and the nature of response functions in thermodynamic systems.

Findings

Environmental influence can suppress divergence of correlation length.

Critical phenomena are relative, depending on environmental context.

Response functions are intrinsic, but critical behavior is environment-dependent.

Abstract

Recently (arXiv:0910.2870), we have derived a fluctuation theorem for systems in thermodynamic equilibrium compatible with anomalous response functions, e.g. the existence of states with \textit{negative heat capacities} $C<0$. In this work, we show that the present approach of the fluctuation theory introduces new insights in the understanding of \textit{critical phenomena}. Specifically, the new theorem predicts that the environmental influence can radically affect critical behavior of systems, e.g. to provoke a suppression of the divergence of correlation length $\xi$ and some of its associated phenomena as spontaneous symmetry breaking. Our analysis reveals that while response functions and state equations are \emph{intrinsic properties} for a given system, critical behaviors are always \emph{relative phenomena}, that is, their existence crucially depend on the underlying environmental influence.