Hack Pedro, Gottwald Sebastian, Braun Daniel A
Institute of Neural Information Processing, Ulm University, 89081 Ulm, Germany.
Entropy (Basel). 2022 Nov 27;24(12):1731. doi: 10.3390/e24121731.
We define common thermodynamic concepts purely within the framework of general Markov chains and derive Jarzynski's equality and Crooks' fluctuation theorem in this setup. In particular, we regard the discrete-time case, which leads to an asymmetry in the definition of work that appears in the usual formulation of Crooks' fluctuation theorem. We show how this asymmetry can be avoided with an additional condition regarding the energy protocol. The general formulation in terms of Markov chains allows transferring the results to other application areas outside of physics. Here, we discuss how this framework can be applied in the context of decision-making. This involves the definition of the relevant quantities, the assumptions that need to be made for the different fluctuation theorems to hold, as well as the consideration of discrete trajectories instead of the continuous trajectories, which are relevant in physics.
我们纯粹在一般马尔可夫链的框架内定义常见的热力学概念，并在此框架下推导雅津斯基等式和克鲁克斯涨落定理。特别地，我们考虑离散时间情形，这导致在克鲁克斯涨落定理的通常表述中出现的功的定义存在不对称性。我们展示了如何通过关于能量协议的附加条件来避免这种不对称性。用马尔可夫链表示的一般表述使得能够将结果转移到物理学之外的其他应用领域。在此，我们讨论这个框架如何能应用于决策背景中。这涉及相关量的定义、为使不同涨落定理成立而需要做出的假设，以及对离散轨迹而非物理学中相关的连续轨迹的考虑。
