Netz Roland R
Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany.
Phys Rev E. 2020 Feb;101(2-1):022120. doi: 10.1103/PhysRevE.101.022120.
A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and nonequilibrium stationary states. An equilibrium system is here defined as a system whose stationary distribution equals the Boltzmann distribution, the relation of this definition to the conditions of detailed balance and vanishing probability current is discussed both for underdamped as well as for overdamped systems. Based on the exactly calculated dynamic approach to the stationary distribution, the functional that governs this approach, which is called the free entropy S_{free}(t), is constructed. For the stationary distribution S_{free}(t) becomes maximal and its time derivative, the free entropy production S[over ̇]{free}(t), is minimal and vanishes. Thus, S{free}(t) characterizes equilibrium as well as nonequilibrium stationary distributions by their extremal and stability properties. For an equilibrium system, i.e., if all heat baths have the same temperature, the free entropy equals the negative free energy divided by temperature and thus corresponds to the Massieu function which was previously introduced in an alternative formulation of statistical mechanics. Using a systematic perturbative scheme for calculating velocity and position correlations in the overdamped massless limit, explicit results for few particles are presented: For two particles localization in position and momentum space is demonstrated in the nonequilibrium stationary state, indicative of a tendency to phase separate. For three elastically interacting particles heat flows from a particle coupled to a cold reservoir to a particle coupled to a warm reservoir if the third reservoir is sufficiently hot. This does not constitute a violation of the second law of thermodynamics, but rather demonstrates that a particle in such a nonequilibrium system is not characterized by an effective temperature which equals the temperature of the heat bath it is coupled to. Active particle models can be described in the same general framework, which thereby allows us to characterize their entropy production not only in the stationary state but also in the approach to the stationary nonequilibrium state. Finally, the connection to nonequilibrium thermodynamics formulations that include the reservoir entropy production is discussed.
一个基于哈密顿量的模型，用于研究许多受线性摩擦作用且与不同温度热库耦合的大量相互作用的有质量粒子，该模型被用于研究向平衡态和非平衡稳态的动态趋近过程。这里将平衡系统定义为其稳态分布等于玻尔兹曼分布的系统，针对欠阻尼以及过阻尼系统，讨论了此定义与细致平衡条件和概率流消失之间的关系。基于对稳态分布精确计算的动态趋近过程，构建了支配该过程的泛函，即自由熵(S_{free}(t))。对于稳态分布，(S_{free}(t))达到最大值，其时间导数，即自由熵产生(S[\dot{]}{free}(t))最小且为零。因此，(S{free}(t))通过其极值和稳定性特性来表征平衡态以及非平衡稳态分布。对于平衡系统，即如果所有热库具有相同温度，自由熵等于负自由能除以温度，因此对应于先前在统计力学的另一种表述中引入的马西厄函数。使用一种系统的微扰方案来计算过阻尼无质量极限下的速度和位置关联，给出了少量粒子的明确结果：对于两个粒子，在非平衡稳态下展示了位置和动量空间中的局域化，这表明存在相分离的趋势。对于三个弹性相互作用的粒子，如果第三个热库足够热，热量会从与冷库耦合的粒子流向与温库耦合的粒子。这并不构成对热力学第二定律的违反，而是表明在这样的非平衡系统中，一个粒子并非由等于其耦合热库温度的有效温度来表征。活性粒子模型可以在相同的一般框架中进行描述，这从而使我们不仅能够表征它们在稳态下的熵产生，还能表征它们在趋近非平衡稳态过程中的熵产生。最后，讨论了与包括热库熵产生的非平衡热力学表述的联系。
