Non-Markovian momentum computing: Thermodynamically efficient and computation universal
Kyle J. Ray, Alexander B. Boyd, Gregory W. Wimsatt, James P. Crutchfield · Physical Review Research · 2021
Practical, useful computations are instantiated via physical processes.Information must be stored and updated within a system's configurations, whose energetics determine a computation's cost.To describe thermodynamic and biological information processing, a growing body of results embraces rate equations as the underlying mechanics of computation.Strictly applying these continuous-time stochastic Markov dynamics, however, precludes a universe of natural computing.Within this framework, operations as simple as a NOT gate (flipping a bit) and swapping two bits, and swapping bits are inaccessible.We show that expanding the toolset to continuoustime hidden Markov dynamics substantially removes the constraints, by allowing information to be stored in a system's latent states.We demonstrate this by simulating computations that are impossible to implement without hidden states.We design and analyze a thermodynamically costless bit flip, providing a counterexample to rateequation modeling.We generalize this to a costless Fredkin gate-a key operation in reversible computing that is Turing complete (computation universal).Going beyond rate-equation dynamics is not only possible but also necessary if stochastic thermodynamics is to become part of the paradigm for physical information processing.