Thermodynamic bounds for diffusion in non-equilibrium systems with multiple timescales

TL;DR

This paper derives a tighter thermodynamic uncertainty relation for Gaussian processes with memory, applicable to non-equilibrium systems with multiple timescales, and demonstrates its effectiveness on granular fluid data.

Contribution

It introduces a new, tighter bound on mean squared displacement for non-equilibrium Gaussian processes with memory, valid at finite times, and applicable to complex many-body systems.

Findings

The bound is tighter than previous relations.

It can distinguish equilibrium from non-equilibrium behavior.

Applied successfully to granular fluid data.

Abstract

We derive a Thermodynamic Uncertainty Relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to previous results and also holds at finite time. We apply our findings to experimental and numerical data for a many-body interacting granular fluid, characterized by regimes of anomalous diffusion. In some cases, our relation can distinguish between equilibrium and non-equilibrium behavior, a non-trivial inference task, particularly for Gaussian processes.