A topological fluctuation theorem

TL;DR

This paper introduces a topological fluctuation theorem showing that entropy production in fluid systems is quantized and governed by a topological invariant, independent of detailed force configurations or distribution shapes.

Contribution

It formulates a novel topological fluctuation theorem based on winding numbers, revealing robustness and quantization of entropy production in fluctuating fluid systems.

Findings

Entropy production is quantized and topologically protected.

The theorem applies to non-Gaussian probability distributions.

Entropy production depends only on winding numbers around vortex cores.

Abstract

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to give a geometric characterization of the entropy production. Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected modes in various classical and quantum systems. We demonstrate that entropy production is quantized in these strongly fluctuating systems, and it is controlled by a topological invariant. We demonstrate that the theorem holds even when the probability distributions are non-Gaussian functions of the generated heat.