Fluctuation Dissipation Relations for Active Field Theories

Abstract

Breakdown of time-reversal symmetry is a defining property of non-equilibrium systems, such as active matter, which is composed of units that consume energy. We employ a formalism that allows us to derive a class of identities associated with the time-reversal transformation in non-equilibrium field theories, in the spirit of Ward-Takahashi identities. We present a generalization of the fluctuation-dissipation theorem valid for active systems as a particular realization of such an identity, and consider its implications and applications for a range of active field theories. The field theoretical toolbox developed here helps to quantify the degree of non-equilibrium activity of complex systems exhibiting collective behavior.

This revised version has been substantially expanded as compared to v1. The entire NRCH section of v1 has been removed in this revision, and submitted to the arxiv separately (arXiv:2502.02524), as an expanded stand-alone manuscript. The title has been slightly revised