Marconi Umberto Marini Bettolo, Puglisi Andrea, Maggi Claudio
Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, 62032, Camerino, INFN Perugia, Italy.
Consiglio Nazionale delle Ricerche-ISC, Rome, Italy.
Sci Rep. 2017 Apr 21;7:46496. doi: 10.1038/srep46496.
Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system's Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.
随机热力学和流体动力学方法被应用于最近引入的活性粒子模型。该模型由一个受到高斯色噪声作用的过阻尼粒子组成。受随机热力学的启发，我们从系统的福克 - 普朗克方程推导出与活性浴的平均热交换和功交换以及相关的熵产生。我们表明克劳修斯不等式成立，其中活性浴的局部（非均匀）温度取代了平衡系统中通常遇到的均匀温度。此外，通过将动力学空间限制在局部分布函数的一阶速度矩上，我们推导出一种流体动力学描述，其中出现了局部压力、动力学温度和内热通量，并且与先前的热力学分析一致。该过程还表明了在哪些条件下可以得到统一色噪声近似（UCNA）：这种近似忽略了向活性浴的快速弛豫，因此产生了细致平衡和零熵产生。在最后一部分，通过使用多时间尺度分析，我们提供了一种确定克莱默斯方程解的建设性方法（UCNA 的替代方法），并且超越了确定负熵产生的细致平衡条件。
