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# Condensed Matter > Statistical Mechanics

# Title: Non-Markovian Momentum Computing: Universal and Efficient

(Submitted on 2 Oct 2020)

Abstract: 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.

## Submission history

From: James P. Crutchfield [view email]**[v1]**Fri, 2 Oct 2020 18:08:26 GMT (308kb,D)

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