A topological fluctuation theorem

Journal article

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.

Authors: Mahault, B; Tang, E; Golestanian, R

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Nature Research
• Journal: Nature Communications
• Volume: 13
• Issue: 1
• Pages: 3036-3036
• Article number: 3036
• Publication date: 2022-05-31
• DOI: 10.1038/s41467-022-30644-6
• EISSN: 2041-1723
• ISSN: 2041-1723
• Language: English
• Keywords: Topology (electrical circuits); Entropy production; Statistical physics; Quantum mechanics; Fluctuation theorem; Physics; Entropy (arrow of time); Probability distribution; Topological quantum number; Topological entropy; Gaussian; Quantum; Mathematics; Pure mathematics; Vortex; Combinatorics; Non-equilibrium thermodynamics