Vo Van Tuan, Van Vu Tan, Hasegawa Yoshihiko
Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
Phys Rev E. 2020 Dec;102(6-1):062132. doi: 10.1103/PhysRevE.102.062132.
The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is available, it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations. Here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes. For a particular case, we show that our universal relation reduces to a classical speed limit, imposing a constraint on the speed of the system's evolution in terms of the Hatano-Sasa entropy production. Notably, the obtained classical speed limit is tighter than the previously reported bound by a constant factor. Moreover, we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation. Our uncertainty relation holds for systems with time-reversal symmetry breaking and recovers several existing bounds. Our approach provides a unified perspective on two closely related classes of inequality: classical speed limits and thermodynamic uncertainty relations.
总熵产生量化了热力学系统中的不可逆程度，对于任何可行的动力学而言，其值均为非负。当有诸如初始和最终状态或可观测量的矩等额外信息可用时，根据经典速度极限和热力学不确定性关系可知，存在更严格的熵产生下限。在此，我们根据可观测量在时间向前和向后过程中的概率分布，获得了总熵产生的一个通用下限。对于一个特定情形，我们表明我们的通用关系简化为一个经典速度极限，根据Hatano-Sasa熵产生对系统的演化速度施加了一个约束。值得注意的是，所得到的经典速度极限比先前报道的界限严格了一个常数因子。此外，我们证明了一个广义的热力学不确定性关系可以从通用关系的另一个特定情形推导出来。我们的不确定性关系适用于具有时间反演对称性破缺的系统，并恢复了几个现有的界限。我们的方法为两类密切相关的不等式：经典速度极限和热力学不确定性关系，提供了一个统一的视角。
