Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter

TL;DR

This paper derives thermodynamic bounds on equilibrium fluctuations of order parameters, applicable to both global and local measurements, enabling inference of system properties from local fluctuation data.

Contribution

It introduces thermodynamic bounds on order parameter fluctuations using isometric fluctuation theorems, applicable to local and global cases, advancing understanding of equilibrium fluctuation constraints.

Findings

Derived bounds for global order parameter fluctuations

Established bounds for local fluctuations in sub-systems

Potential to infer symmetry breaking fields from local data

Abstract

We analyze thermodynamic bounds on equilibrium fluctuations of an order parameter, which are analogous to relations, which have been derived recently in the context of non-equilibrium fluctuations of currents. We discuss the case of {\it global} fluctuations when the order parameter is measured in the full system of interest, and {\it local} fluctuations, when the order parameter is evaluated only in a sub-part of the system. Using isometric fluctuation theorems, we derive thermodynamic bounds on the fluctuations of the order parameter in both cases. These bounds could be used to infer the value of symmetry breaking field or the relative size of the observed sub-system to the full system from {\it local} fluctuations.