A definition of nonequilibrium free energy $\mathcal{F}_{\textsc{s}}$ is proposed for dynamical Gaussian quantum open systems strongly coupled to a heat bath and a formal derivation is provided by way of the generating functional in terms of the coarse-grained effective action and the influence action. For Gaussian open quantum systems exemplified by the quantum Brownian motion model studied here, a time-varying effective temperature can be introduced in a natural way, and with it, the nonequilibrium free energy $\mathcal{F}_{\textsc{s}}$, von Neumann entropy $\mathcal{S}_{vN}$ and internal energy $\mathcal{U}_{\textsc{s}}$ of the reduced system ($S$) can be defined accordingly. In contrast to the nonequilibrium free energy found in the literature which references the bath temperature, the nonequilibrium thermodynamic functions we find here obey the familiar relation $\mathcal{F}_{\textsc{s}}(t)=\mathcal{U}_{\textsc{s}}(t)- T_{\textsc{eff}} (t)\,\mathcal{S}_{vN}(t)$ {\it at any and all moments of time} in the system's fully nonequilibrium evolution history. After the system equilibrates they coincide, in the weak coupling limit, with their counterparts in conventional equilibrium thermodynamics. Since the effective temperature captures both the state of the system and its interaction with the bath, upon the system's equilibration, it approaches a value slightly higher than the initial bath temperature. Notably, it remains nonzero for a zero-temperature bath, signaling the existence of system-bath entanglement. Reasonably, at high bath temperatures and under ultra-weak couplings, it becomes indistinguishable from the bath temperature. The nonequilibrium thermodynamic functions and relations discovered here for dynamical Gaussian quantum systems should open up useful pathways toward establishing meaningful theories of nonequilibrium quantum thermodynamics.
Coarsening and Aging of Lattice Polymers: Influence of Bond Fluctuations
我们提出的非平衡动力学的崩溃模型灵活的均聚物与固定和波动的单体之间的键简单立方晶格的结果。从我们的蒙特卡罗模拟的结果表明，唯象，在崩溃过程中观察到的事件序列是独立的键标准。虽然在不同温度下的集群（单体）的增长表现出非普适的幂律行为时，债券是固定的，通过考虑对角键的存在下，在债券中引入波动产生的温度无关的增长，这可以描述一个通用的非平衡有限尺寸标度函数与非普适度量因子。我们还研究了相关的老化现象，探测一个合适的两次密度密度自相关函数显示一个简单的幂律缩放相对于不断增长的集群大小。然而，与团簇增长指数$α_c $不同，控制塌缩期间老化的非平衡自相关指数$λ_C$与键类型无关，并且在所有温度下严格遵循我们两人在Phys. Rev. E 93，032506（2016）中提出的界限。
Shape, orientation and magnitude of the curl quantum flux, the coherence and the statistical correlations in energy transport at nonequilibrium steady state
Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
通过与标量势$V(\vec r)$和矢量势$\vec A(\vec r)$中的非厄米量子力学的对应，重新讨论了在$N$维的任意力场$\vec f(\vec r)$中的非平衡Fokker-Planck动力学.不可逆性的相关参数是$\frac{N(N-1)}{2}$磁矩阵元$B_{nm}(\vec x ) =-B_{mn} (\vec x ) = \partial_n A_m (\vec x ) - \partial_m A_n (\vec x )$，而探索矢量势$\vec A(\vec r) $的相应规范变换是有启发性的。这种量子解释对于研究随机轨道的所有时间可加观测量的统计更有成效，因为它们的生成函数对应于具有附加标量和/或矢量势的相同量子问题。我们的主要结论是，分析其大偏差的性质和相应的Doob条件过程的建设可以大大简化通过选择一个适当的规范为每一个目的。这个一般的框架，然后应用到特殊的时间添加剂的观测量的奥恩斯坦-乌伦贝克轨迹在维度$N$，其生成函数对应于量子传播涉及二次标量势和线性矢量势，即量子谐振子在恒定的磁性矩阵。作为简单的说明性例子，我们最后集中在布朗回转器的尺寸$N=2$，以计算其随机轨迹的熵产生的大偏差性质，并构造相应的条件过程具有给定的值的熵产生每单位时间。
我们描述了一种策略，以提高自由能估计的效率，通过减少耗散非平衡蒙特卡罗模拟。该策略概括了目标自由能微扰方法[Phys. Rev. E. 65，046122，2002]的非平衡切换模拟，并涉及通过耦合系统的演变，外部工作参数的更新，生成人工的，“护送”的轨迹。我们的主要结果是：（1）护送轨线的广义涨落定理;（2）自由能差Δ F的估计。我们说明的方法和模型系统的有效性。
Nonequilibrium full counting statistics of multicomponent strongly-interacting quantum gases with defects
Institute for Space Sciences（空间科学研究所）；London Institute for Mathematical Sciences, Royal Institution（伦敦数学科学研究所，皇家学会）；Department of Physics, University of Oradea（奥拉迪亚大学物理系）；Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics（布达佩斯技术与经济大学物理学院理论物理系）；MTA-BME Lendület “Momentum” Open Quantum Systems Research Group, Budapest University of Technology and Economics（布达佩斯技术与经济大学 MTA-BME 领导力“动量”开放量子系统研究组）
