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A topological fluctuation theorem.

Benoît Mahault¹, Evelyn Tang¹, Ramin Golestanian^2,3

¹Max Planck Institute for Dynamics and Self-Organization, 37077, Göttingen, Germany.

Nature Communications

|May 31, 2022

Summary

This summary is machine-generated.

This study reveals that entropy production in fluids can be quantized and controlled by topology. A new topological fluctuation theorem shows probabilities are robust to trajectory changes, even with non-Gaussian heat distributions.

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Area of Science:

Thermodynamics
Fluid Dynamics
Topology

Background:

Second law of thermodynamics traditionally implies non-negative entropy production.
Fluctuation theorems allow for non-zero probabilities of observing negative entropy production.
Stokes theorem provides a geometric framework for entropy production in fluid particle trajectories.

Purpose of the Study:

To formulate a topological fluctuation theorem for entropy production in fluids.
To investigate the role of topology, specifically winding numbers, in characterizing entropy production.
To demonstrate the robustness and quantization of entropy production in fluctuating systems.

Main Methods:

Formulating a topological fluctuation theorem based on vortex core winding numbers.
Analyzing the geometric characterization of entropy production using Stokes theorem.
Examining the probability distributions of entropy production, including non-Gaussian cases.

Main Results:

A topological fluctuation theorem was formulated, dependent only on winding numbers.
Entropy production was shown to be quantized and controlled by a topological invariant.
The theorem demonstrated robustness against local trajectory deformations and non-Gaussian heat distributions.

Conclusions:

Topological properties, specifically winding numbers, govern entropy production in fluctuating fluid systems.
Entropy production is quantized in these systems, offering a new perspective beyond classical thermodynamics.
The developed theorem provides a robust framework for understanding entropy production in complex, fluctuating environments.