Recent studies have experienced the acceleration of convergence in Markov chain Monte Carlo methods implemented by the systems without detailed balance condition (DBC). However, such advantage of the violation of DBC has not been confirmed in general. We investigate the effect of the absence of DBC on the convergence toward equilibrium. Surprisingly, it is shown that the DBC violation always makes the relaxation faster. Our result implies the existence of a kind of thermodynamic inequality that connects the nonequilibrium process relaxing toward steady state with the relaxation process which has the same probability distribution as its equilibrium state.
A measure of the violation of the 'detailed balance' criterion: a possible definition of a 'distance' from equilibrium
受R. K. P. Zia和B. Schmittmann，J. Stat. P07012（2007）中，我们提出通过概率流形成的矩阵的$p$ -范数（$||K||_p$）来测量对“细致平衡”准则的违反。它的渐近分析，完全不对称的排斥过程，激发了一个“距离”的定义，从平衡$K^*$获得$p=1$。此外，我们表明，后者的数量和平均活动$A^*$都与熵产生的概率分布。最后，考虑到开放ASEP和开放ZRP，我们表明，粒子的电流给出了一个精确的措施违反“细致平衡”。
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）
Large deviations for the Skew-Detailed-Balance Lifted-Markov processes to sample the equilibrium distribution of the Curie-Weiss model
在蒙特卡洛采样领域中为了加速相对于细致平衡动力学向稳态的收敛而提出的打破细致平衡的马尔可夫链中，“提升”的思想在于将配置空间复制成两个副本$σ=\pm$，并且在每个副本中施加有向流，以便更有效地探索配置空间。K. S. Turitsyn，M. Chertkov和M. Vucelja [Physica D Nonlinear Phenomena 240，410（2011）]重新访问Curie-Weiss平均场铁磁模型，其中磁化的动力学是封闭的。分析了经验时间平均观测量在不同水平上的大偏差，并与它们的细致平衡对应物进行了比较，无论是对于离散的广泛磁化$M$还是对于大系统尺寸$N$的连续的强磁化$m=\frac{M}{N}$。
