Stochastic network dynamics are typically assumed to be memoryless. Involving prolonged dwells interrupted by instantaneous transitions between nodes, such Markov networks stand as a coarse-graining paradigm for chemical reactions, gene expression, molecular machines, spreading of diseases, protein dynamics, diffusion in energy landscapes, epigenetics, and many others. However, as soon as transitions cease to be negligibly short, as often observed in experiments, the dynamics develops a memory. That is, state changes depend not only on the present state but also on the past. Here, we establish the first thermodynamically consistent—dissipation-preserving—mapping of continuous dynamics onto a network, which reveals ingrained dynamical symmetries and an unforeseen kinetic hysteresis. These symmetries impose three independent sources of fluctuations in state-to-state kinetics that determine the “flavor of memory.” The hysteresis between the forward- or backward-in-time coarse graining of continuous trajectories implies a new paradigm for the thermodynamics of active molecular processes in the presence of memory, that is, beyond the assumption of local detailed balance. Our results provide a new understanding of fluctuations in the operation of molecular machines as well as catch bonds involved in cellular adhesion.

中文翻译：

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强驱动网络中的紧急记忆和动力学滞后

通常假设随机网络动态是无记忆的。涉及由节点之间的瞬时转换中断的长时间驻留，这种马尔可夫网络是化学反应、基因表达、分子机器、疾病传播、蛋白质动力学、能量景观扩散、表观遗传学等的粗粒度范式。然而，一旦转换不再像在实验中经常观察到的那样短得可以忽略不计，动态就会产生记忆。也就是说，状态变化不仅取决于当前状态，还取决于过去。在这里，我们建立了第一个热力学一致的——耗散保持——将连续动力学映射到网络上，这揭示了根深蒂固的动力学对称性和不可预见的动力学滞后。这些对称性在决定“记忆味道”的状态间动力学中强加了三个独立的波动来源。连续轨迹在时间上向前或向后粗粒度化之间的滞后意味着存在记忆时活性分子过程的热力学的新范式，也就是说，超出了局部详细平衡的假设。我们的结果提供了对分子机器运行波动以及细胞粘附所涉及的捕获键的新理解。超出局部详细平衡的假设。我们的结果提供了对分子机器运行波动以及细胞粘附所涉及的捕获键的新理解。超出局部详细平衡的假设。我们的结果提供了对分子机器运行波动以及细胞粘附所涉及的捕获键的新理解。