Murashita Yûto, Esposito Massimiliano
Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan.
Complex Systems and Statistical Mechanics, Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg.
Phys Rev E. 2016 Dec;94(6-1):062148. doi: 10.1103/PhysRevE.94.062148. Epub 2016 Dec 29.
After establishing stochastic thermodynamics for underdamped Langevin systems in contact with multiple reservoirs, we derive its overdamped limit using timescale separation techniques. The overdamped theory is different from the naive theory that one obtains when starting from overdamped Langevin or Fokker-Planck dynamics and only coincides with it in the presence of a single reservoir. The reason is that the coarse-grained fast momentum dynamics reaches a nonequilibrium state, which conducts heat in the presence of multiple reservoirs. The underdamped and overdamped theory are both shown to satisfy fundamental fluctuation theorems. Their predictions for the heat statistics are derived analytically for a Brownian particle on a ring in contact with two reservoirs and subjected to a nonconservative force and are shown to coincide in the long-time limit.
在为与多个热库接触的欠阻尼朗之万系统建立随机热力学之后，我们使用时间尺度分离技术推导其过阻尼极限。过阻尼理论不同于从过阻尼朗之万或福克 - 普朗克动力学出发时得到的朴素理论，并且仅在存在单个热库的情况下与之相符。原因是粗粒化的快速动量动力学达到非平衡态，在存在多个热库时会传导热量。结果表明，欠阻尼和过阻尼理论都满足基本涨落定理。对于与两个热库接触且受到非保守力的环上布朗粒子，我们通过解析方法推导了它们对热统计量的预测，并表明在长时间极限下两者相符。
