接触驱动系统粒子密度的非加性大偏差函数
Non-additive large deviations function for the particle densities of driven systems in contact
摘要：
研究了两个定态驱动系统中粒子以消失速率交换时的粒子密度的非平衡大偏差函数。我们首先通过系统的多尺度分析，推导出每个系统中粒子数分布所满足的粗粒度主方程。假设这种分布对于大系统采取大偏差形式，我们得到密度的大偏差函数所满足的方程（类似于Hamilton-Jacobi方程）。取决于所考虑的系统，该方程可以满足或不满足宏观细致平衡性质，即，大偏差水平下的时间可逆性。在不存在宏观细致平衡的情况下，大偏差函数可以确定为接近满足宏观细致平衡的解的展开式。在这种情况下，大偏差函数一般是非加性的，即，它不能被分成两个单独的贡献，从每个系统。此外，大偏差函数可以被解释为非平衡自由能，因为它满足热力学第二定律的推广，在Hatano-Sasa关系的精神。部分结果在精确可解的驱动格子气模型上得到了说明。
英文摘要：
We investigate the non-equilibrium large deviations function of the particle densities in two steady-state driven systems exchanging particles at a vanishing rate. We first derive through a systematic multi-scale analysis the coarse-grained master equation satisfied by the distribution of the numbers of particles in each system. Assuming that this distribution takes for large systems a large deviations form, we obtain the equation (similar to a Hamilton-Jacobi equation) satisfied by the large deviations function of the densities. Depending on the systems considered, this equation may satisfy or not the macroscopic detailed balance property, i.e., a time-reversibility property at large deviations level. In the absence of macroscopic detailed balance, the large deviations function can be determined as an expansion close to a solution satisfying macroscopic detailed balance. In this case, the large deviations function is generically non-additive, i.e., it cannot be split as two separate contributions from each system. In addition, the large deviations function can be interpreted as a non-equilibrium free energy, as it satisfies a generalization of the second law of thermodynamics, in the spirit of the Hatano-Sasa relation. Some of the results are illustrated on an exactly solvable driven lattice gas model.
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