Mahault Benoît, Tang Evelyn, Golestanian Ramin
Max Planck Institute for Dynamics and Self-Organization, 37077, Göttingen, Germany.
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3PU, UK.
Nat Commun. 2022 May 31;13(1):3036. doi: 10.1038/s41467-022-30644-6.
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.
涨落定理规定了观察到负熵产生的非零概率，这与热力学第二定律的朴素预期相反。对于流体中封闭的粒子轨迹，斯托克斯定理可用于给出熵产生的几何特征。基于此图景，我们提出了一个拓扑涨落定理，它仅取决于围绕每个涡旋核心的缠绕数，并且对力的其他方面不敏感。该概率对粒子轨迹的局部变形具有鲁棒性，这让人联想到各种经典和量子系统中的拓扑保护模式。我们证明，在这些强涨落系统中熵产生是量子化的，并且它由一个拓扑不变量控制。我们证明，即使概率分布是所产生热量的非高斯函数，该定理仍然成立。
