# Fluctuation Relation for the Dissipative Flux: The Role of Dynamics, Correlations and Heat Baths

## TL;DR

This paper explores how different physical systems satisfy the fluctuation relation in nonequilibrium physics, focusing on heat transport and the role of system dynamics and heat baths.

## Contribution

The study reveals that different lattice models satisfy the fluctuation relation through distinct mechanisms, influenced by heat conduction properties and observation time.

## Key findings

- Systems with normal heat conduction, like the lattice ϕ4 model, satisfy the fluctuation relation after a certain observation time, regardless of size.
- Anomalous heat conductors require longer observation times, especially as lattice size increases, due to heat bath fluctuations affecting the system.
- The current autocorrelation function helps identify the conditions under which systems align with the fluctuation relation.

## Abstract

The fluctuation relation stands as a fundamental result in nonequilibrium statistical physics. Its derivation, particularly in the stationary state, places stringent conditions on the physical systems of interest. On the other hand, numerical analyses usually do not directly reveal any specific connection with such physical properties. This study proposes an investigation of such a connection with the fundamental ingredients of the derivation of the fluctuation relation for the dissipation, which includes the decay of correlations, in the case of heat transport in one-dimensional systems. The role of the heat baths in connection with the system’s inherent properties is then highlighted. A crucial discovery of our research is that different lattice models obeying the steady-state fluctuation relation may do so through fundamentally different mechanisms, characterizing their intrinsic nature. Systems with normal heat conduction, such as the lattice ϕ4 model, comply with the theorem after surpassing a certain observational time window, irrespective of lattice size. In contrast, systems characterized by anomalous heat conduction, such as Fermi–Pasta–Ulam–Tsingou-β and harmonic oscillator chains, require extended observation periods for theoretical alignment, particularly as the lattice size increases. In these systems, the heat bath’s fluctuations significantly influence the entire lattice, linking the system’s fluctuations with those of the bath. Here, the current autocorrelation function allows us to discern the varying conditions under which different systems satisfy with the fluctuation relation. Our findings significantly expand the understanding of the stationary fluctuation relation and its broader implications in the field of nonequilibrium phenomena.