All computation is physically embedded. Reflecting this, a growing body of results embraces rate equations as the underlying mechanics of thermodynamic computation and biological information processing. Strictly applying the implied continuous-time Markov chains, however, excludes a universe of natural computing. We show that expanding the toolset to continuous-time hidden Markov chains substantially removes the constraints. The general point is made concrete by our analyzing two eminently-useful computations that are impossible to describe with a set of rate equations over the memory states. We design and analyze a thermodynamically-costless bit flip, providing a first counterexample to rate-equation modeling. We generalize this to a costless Fredkin gate---a key operation in reversible computing that is computation universal. Going beyond rate-equation dynamics is not only possible, but necessary if stochastic thermodynamics is to become part of the paradigm for physical information processing.

中文翻译：

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非马尔可夫动量计算：通用且高效

所有计算都是物理嵌入的。反映这一点，越来越多的结果将速率方程作为热力学计算和生物信息处理的基础机制。然而，严格应用隐含的连续时间马尔可夫链，排除了自然计算的领域。我们表明，将工具集扩展到连续时间隐马尔可夫链可以大大消除约束。通过我们分析两个非常有用的计算，不可能用一组关于记忆状态的速率方程来描述一般的观点。我们设计并分析了热力学无成本的位翻转，为速率方程建模提供了第一个反例。我们将其推广到无成本的 Fredkin 门——可逆计算中的一个关键操作，它是计算通用的。