The hidden fluctuation-dissipation theorem for growth

TL;DR

This paper uncovers a hidden fluctuation-dissipation theorem (FDT) for growth processes, extending the concept beyond diffusion and explaining FDT violations through hierarchical theorems in statistical mechanics.

Contribution

It introduces a hidden FDT for growth phenomena and correlated noise, expanding the applicability of FDT in non-diffusive processes.

Findings

A hidden FDT exists for growth processes.

Correlated noise growth also exhibits a similar FDT form.

Hierarchy of statistical mechanics explains FDT violations.

Abstract

In a stochastic process, where noise is always present, the fluctuation-dissipation theorem (FDT) becomes one of the most important tools in statistical mechanics and, consequently, it appears everywhere. Its major utility is to provide a simple response to study certain processes in solids and fluids. However, in many situations we are not talking about a FDT, but about the noise intensity. For example, noise has enormous importance in diffusion and growth phenomena. Although we have an explicit FDT for diffusion phenomena, we do not have one for growth processes where we have a noise intensity. We show that there is a hidden FDT for the growth phenomenon, similar to the diffusive one. Moreover, we show that growth with correlated noise presents as well a similar form of FDT. We also call attention to the hierarchy within the theorems of statistical mechanics and how this explains the violation of the FDT in some phenomena.