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Abstract

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.