DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
CNRS, LIPhy, Université Grenoble Alpes, F-38000 Grenoble, France.
J Chem Phys. 2019 Mar 7;150(9):094108. doi: 10.1063/1.5085740.
We discuss the notion of the nonequilibrium chemical potential in gases of non-interacting active particles filling two compartments separated by a potential energy barrier. Different types of active particles are considered: run-and-tumble particles, active Brownian particles, and active Brownian particles with a stochastic reorientation along an external field. After recalling some analytical results for run-and-rumble particles in one dimension, we focus on the two-dimensional case and obtain a perturbative expression of the density profile in the limit of a fast reorientation dynamics, for the three models of active particles mentioned above. Computing the chemical potentials of the nonequilibrium systems in contact from the knowledge of the stationary probability distribution of the whole system-which agrees with a recently proposed general definition of the chemical potential in nonequilibrium systems in contact-we, generically, find that the chemical potential lacks an equation of state in the sense that it depends on the detailed shape of the potential energy barrier separating the compartments and not only on bulk properties, at odds with equilibrium. This situation is reminiscent of the properties of the mechanical pressure in active systems. We also argue that the Maxwell relation is no longer valid and cannot be used to infer the nonequilibrium chemical potential from the knowledge of the mechanical pressure.
我们讨论了在由势能屏障分隔的两个隔室中充满非相互作用的活性粒子的气体中的非平衡化学势的概念。考虑了不同类型的活性粒子：跑-跌粒子、主动布朗粒子和沿外场随机重新取向的主动布朗粒子。在回忆了一维中关于跑-跌粒子的一些分析结果之后，我们专注于二维情况，并为上述三种主动粒子模型获得了快速重定向动力学极限下密度分布的微扰表达式。从整个系统的稳态概率分布中计算接触的非平衡系统的化学势——这与最近提出的接触中非平衡系统化学势的一般定义一致——我们通常发现化学势缺乏状态方程的性质，即它取决于分隔隔室的势能屏障的详细形状，而不仅仅是体积性质，与平衡情况不一致。这种情况让人联想到主动系统中机械压力的特性。我们还认为，麦克斯韦关系不再有效，不能从机械压力的知识推断非平衡化学势。
