DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France.
Phys Rev E. 2019 Nov;100(5-1):052125. doi: 10.1103/PhysRevE.100.052125.
We introduce a general framework to describe the stationary state of two driven systems exchanging particles or mass through a contact, in a slow exchange limit. The definition of chemical potentials for the systems in contact requires that the large-deviation function describing the repartition of mass between the two systems is additive, in the sense of being a sum of contributions from each system. We show that this additivity property does not hold for an arbitrary contact dynamics, but is satisfied on condition that a macroscopic detailed balance condition holds at contact, and that the coarse-grained contact dynamics satisfies a factorization property. However, the nonequilibrium chemical potentials of the systems in contact keep track of the contact dynamics, and thus do not obey an equation of state. These nonequilibrium chemical potentials can be related either to the equilibrium chemical potential, or to the nonequilibrium chemical potential of the isolated systems. Results are applied both to an exactly solvable driven lattice gas model and to the Katz-Lebowitz-Spohn model using a numerical procedure to evaluate the chemical potential. The breaking of the additivity property is also illustrated on the exactly solvable model.
我们引入了一个通用框架来描述通过接触交换粒子或质量的两个驱动系统的静止状态，在缓慢交换极限下。接触系统的化学势的定义要求描述两个系统之间的质量分配的大偏差函数是可加的，即在每个系统的贡献之和的意义上。我们表明，这种可加性性质不适用于任意接触动力学，而是在接触处满足宏观详细平衡条件并且粗粒化接触动力学满足因式分解性质的条件下成立。然而，接触系统的非平衡化学势跟踪接触动力学，因此不服从状态方程。这些非平衡化学势可以与平衡化学势或孤立系统的非平衡化学势相关联。结果适用于一个完全可解的驱动晶格气体模型和 Katz-Lebowitz-Spohn 模型，使用数值程序来评估化学势。在完全可解模型上也说明了可加性的破坏。
