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Statistical mechanics of a nonequilibrium steady-state classical particle system driven by a constant external force

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Communications in Theoretical Physics 2020年第11期72卷 104-108页

作者：姚婕王延颋 CAS Key Laboratory of Theoretical Physics Institute of Theoretical PhysicsChinese Academy of Sciences55 East Zhongguancun RoadPO Box 2735Beijing100190 China School of Physical Sciences University of Chinese Academy of Sciences19A Yuquan RoadBeijing 100049China

A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time.In this work,the statistical mechanics of such a system is derived solely based on the equiprobability and ergodicity principles,free from any conclusions drawn on equilibrium statistical mechanics or local equilibrium hypothesis.The momentum space distribution is determined by a random walk argument,and the position space distribution is determined by employing the equiprobability and ergodicity principles.The expressions for energy,entropy,free energy,and pressures are then deduced,and the relation among external force,drift velocity,and temperature is also established.Moreover,the relaxation towards its equilibrium is found to be an exponentially decaying process obeying the minimum entropy production theorem.

关键词： nonequilibrium steady state constant external force dissipation statistical mechanics

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Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

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Science China(Physics,Mechanics & Astronomy) 2022年第5期65卷 21-33页

作者： Jin-Min Liang Shi-Jie Wei Shao-Ming Fei School of Mathematical Sciences Capital Normal UniversityBeijing J00048China Beijing Academy of Quantum Information Sciences Beijing 100193China state Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics Tsinghua UniversityBeijing 100084China Shenzhen Institute for Quantum Science and Engineering Southern University of Science and TechnologyShenzhen 518055China

The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks,which is an optimization algorithm for finding a local minimum of an objective function.The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions.Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism,we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems.Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states.Moreover,we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications,by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians.Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications.

关键词： quantum simulation quantum gradient descent algorithm nonequilibrium steady state quantum open system

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Stochastic physics, complex systems and biology

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Frontiers of Electrical and Electronic Engineering in China 2013年第1期8卷 50-53页

作者： Hong Qian Department of Applied Mathematics University of Washington Seattle WA 98195 USA

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod＇s necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated equilibria, spontaneous random ＂mutations＂ and ＂adaptations＂. On an evolutionary time scale it produces sustainable diversity among individuals in a homogeneous population rather than convergence as usually predicted by a deterministic dynamics. The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a perspective.

关键词： Stochastic Dynamic Evolutionary Time Scale nonequilibrium steady state nonequilibrium Phase Transition Stochastic Gene Expression

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