Current fluctuations for the boundary-driven zero-range process on graphs: microscopic versus macroscopic approach and a theory of non-reversible resistor-like networks
Davide Gabrielli, Rosemary J. Harris
备注：
37 pages, 6 figures; minor corrections, to appear on Annales Henri Poincaré
We compute the joint large deviation rate functional in the limit of large time for the current flowing through the edges of a finite graph on which a boundary-driven system of stochastic particles evolves with zero-range dynamics.This generalizes one-dimensional results previously obtained with different approaches; our alternative techniques illuminate various connections and complementary perspectives. In particular, we here use a variational approach to derive the rate functional by contraction from a level 2.5 large deviation rate functional. We perform an exact minimization and finally obtain the rate functional as a variational problem involving a superposition of cost functions for each edge. The contributions from different edges are not independent since they are related by the values of a potential function on the nodes of the graph. The rate functional on the graph is a microscopic version of the continuous rate functional predicted by the macroscopic fluctuation theory, and we indeed show a convergence in the scaling limit. If we split the graph into two connected regions by a cutset and are interested just in the current flowing through the cutset, we find that the result is the same as that of an effective system composed of only one effective edge (as happens at macroscopic level and is expected also for other models). The characteristics of this effective edge are related to the ``capacities'' of the graph and can be obtained by a reduction using elementary transformations as in electrical networks; specifically, we treat components in parallel, in series, and in $N$-star configurations (reduced to effective complete $N$-graphs). Our reduction procedure is directly related to the reduction to the trace process and, since the dynamics is in general not reversible, it is also closely connected to the theory of non-reversible electrical networks.
Linking Microscopic Reversibility to Macroscopic Irreversibility, Emphasizing the Role of Deterministic Thermostats and Simple Examples, At and Away From Equilibrium
Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科学与技术大学基础与前沿科学学院）；University of Electronic Science and Technology of China（电子科学与技术大学）；School of Physics, University of Electronic Science and Technology of China（电子科学与技术大学物理学院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（量子物理与光子量子信息重点实验室）；Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（四川省非经典信息科学基础学科研究中心）
Fundamental Work Scaling and Non-Extensivity in Critical Engines
Pontificia Universidad Católica de Valparaíso（智利天主教瓦帕莱索大学）；Universidad Técnica Federico Santa María（费德里科·圣玛丽亚理工大学）；Universidad San Sebastián（塞巴斯蒂安大学）；Universidad de La Frontera（拉弗龙特拉大学）；Universidad Central de Chile（智利中央大学）
