Fluctuation theorem anomaly in a point-vortex fluid

TL;DR

This paper investigates the fluctuation theorem in a point-vortex fluid, revealing that long-range interactions cause anomalies in entropy production, which are mitigated by adding noise to the system.

Contribution

It demonstrates the conditions under which the fluctuation theorem holds or breaks down in a vortex fluid with long-range interactions and negative temperature states.

Findings

Fluctuation theorem broadly holds at negative temperatures.

Long-range interactions cause large short-term entropy fluctuations.

Adding noise restores the fluctuation theorem's predictions.

Abstract

The second law of thermodynamics posits that in closed macroscopic systems the rate of entropy production must be positive. However, small systems can exhibit negative entropy production over short timescales, seemingly in contradiction with this law. The fluctuation theorem quantitatively connects these two limits, predicting that entropy producing trajectories become exponentially dominant as the system size and measurement time are increased. Here we explore the predictions of the fluctuation theorem for a fluid of point-vortices, where the long-range interactions and existence of negative absolute temperature states provide an intriguing test bed for the theorem. Our results suggest that while the theorem broadly holds even at negative absolute temperatures, the long-range interactions inherent to the vortex matter lead to anomalously large entropy production over short time intervals. The predictions of the fluctuation theorem are only fully recovered when sufficient noise is introduced to the dynamics to overwhelm the vortex-vortex interactions.