轨迹类涨落定理

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Gregory Wimsatt, Alexander B. Boyd, James P. Crutchfield
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引用次数: 0

摘要

轨迹类涨落定理(TCFT)描述了平衡-稳态非平衡过程中热力学量(如功成本和自由能变化)与系统状态轨迹类的概率之间的等式。从概念上讲,TCFT统一了许多先前建立的波动定理,从克鲁克斯的详细波动定理(单轨迹)到Jarzynski不等式(全轨迹集合)。利用关于系统如何演化的粗粒度信息,TCFT为热力学第二定律提供了实质性的加强——事实上,热力学第二定律可能是必要功和自由能变化之间的一个相当弱的界限。它还可以用于改进自由能的经验估计,这是一项众所周知的具有统计学挑战性的任务,通过将注意力从方便但高度不平衡的过程中罕见的,以功为主的轨迹转移开来。TCFT还揭示了新的自由能形式,当计算微观细节难以确定的系统时,这些形式可以解析求解和实际估计,这对约束功成本很有用。对于更普遍的工程系统,它将系统功能中系统状态轨迹的角色与发展这些轨迹所需的特定工作成本联系起来。以前,TCFT被用于将实验实现的约瑟夫森结信息引擎的微观动力学与信息处理方式的介观描述联系起来。这里的发展证明了这一实证分析,阐明了其数学基础。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Trajectory Class Fluctuation Theorem

The Trajectory Class Fluctuation Theorem (TCFT) presents equalities between thermodynamic quantities, such as work costs and free energy changes, and the probabilities of classes of system-state trajectories in equilibrium-steady-state nonequilibrium processes. Conceptually, the TCFT unifies a host of previously-established fluctuation theorems, interpolating from Crooks’ Detailed Fluctuation Theorem (single trajectories) to Jarzynski’s Equality (full trajectory ensembles). Leveraging coarse-grained information about how systems evolve, the TCFT provides a substantial strengthening of the Second Law of Thermodynamics—that, in point of fact, can be a rather weak bound between requisite work and free energy change. It also can be used to improve empirical estimates of free energies, a task known to be statistically challenging, by diverting attention from rare, work-dominant trajectories in convenient but highly nonequilibrium processes. The TCFT also reveals new forms of free energy useful for bounding work costs when computing with systems whose microscopic details are difficult to ascertain—forms that can be solved analytically and practically estimated. For engineered systems more generally, it connects the role of system state trajectories in system functionality to the particular work costs required to evolve those trajectories. Previously, the TCFT was used to connect the microscopic dynamics of experimentally-implemented Josephson-junction information engines with the mesoscopic descriptions of how information was processed. The development here justifies that empirical analysis, explicating its mathematical foundations.

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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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