麦克斯韦棘轮的功能热力学：模式的建构与解构，随机化与去随机化行为
Functional Thermodynamics of Maxwellian Ratchets: Constructing and Deconstructing Patterns, Randomizing and Derandomizing Behaviors
摘要：
麦克斯韦棘轮是自治的，有限状态的热力学引擎，实现输入输出信息转换。以前对这些“恶魔”的研究集中在它们如何利用环境资源来产生功：它们随机化有序输入，利用增加的香农熵将能量从热库转移到功库，同时尊重Liouvillian状态空间动力学和第二定律。然而，到目前为止，正确地确定这种功能热力学操作制度仅限于极少数的发动机，其信息承载自由度之间的相关性可以精确计算，并以封闭的形式-一个高度限制的集合。此外，棘轮行为的一个关键的第二个维度在很大程度上被忽视了--棘轮不仅仅改变了环境输入的随机性，它们的操作结构和解构模式。为了解决这两个方面，我们适应最近的结果，从动态系统和遍历理论，有效地和准确地计算熵率和统计复杂性发散率的一般隐马尔可夫过程。在音乐会与信息处理第二定律，这些方法准确地确定热力学操作制度的有限状态麦克斯韦恶魔任意数量的状态和过渡。此外，它们有助于分析给定引擎的结构与随机性的权衡。其结果是大大增强了对信息引擎的信息处理能力的看法。作为应用，我们对Mandal-Jarzynski棘轮进行了深入的分析，证明了它具有不可数无限的有效状态空间。
英文摘要：
Maxwellian ratchets are autonomous, finite-state thermodynamic engines that implement input-output informational transformations. Previous studies of these "demons" focused on how they exploit environmental resources to generate work: They randomize ordered inputs, leveraging increased Shannon entropy to transfer energy from a thermal reservoir to a work reservoir while respecting both Liouvillian state-space dynamics and the Second Law. However, to date, correctly determining such functional thermodynamic operating regimes was restricted to a very few engines for which correlations among their information-bearing degrees of freedom could be calculated exactly and in closed form---a highly restricted set. Additionally, a key second dimension of ratchet behavior was largely ignored---ratchets do not merely change the randomness of environmental inputs, their operation constructs and deconstructs patterns. To address both dimensions, we adapt recent results from dynamical-systems and ergodic theories that efficiently and accurately calculate the entropy rates and the rate of statistical complexity divergence of general hidden Markov processes. In concert with the Information Processing Second Law, these methods accurately determine thermodynamic operating regimes for finite-state Maxwellian demons with arbitrary numbers of states and transitions. In addition, they facilitate analyzing structure versus randomness trade-offs that a given engine makes. The result is a greatly enhanced perspective on the information processing capabilities of information engines. As an application, we give a thorough-going analysis of the Mandal-Jarzynski ratchet, demonstrating that it has an uncountably-infinite effective state space.
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