Non-Markovian Momentum Computing: Universal and Efficient

Author(s): Ray, Kyle J; Wimsatt, Gregory W; Boyd, Alexander B; Crutchfield, James P | 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.

[1]  M. Esposito,et al.  Non-Markovianity and negative entropy production rates. , 2018, Physical review. E.

[2]  Yoshihiko Hasegawa,et al.  Fluctuation Theorem Uncertainty Relation. , 2019, Physical review letters.

[3]  U. Seifert,et al.  Large deviation function for a driven underdamped particle in a periodic potential. , 2017, Physical review. E.

[4]  David H. Wolpert,et al.  Number of hidden states needed to physically implement a given conditional distribution , 2017, New Journal of Physics.

[5]  M. N. Bera,et al.  Thermodynamics from Information , 2018, 1805.10282.

[6]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[7]  T. Brandes,et al.  Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping , 2016, 1602.01340.

[8]  U. Seifert.  Stochastic thermodynamics, fluctuation theorems and molecular machines , 2012, Reports on progress in physics. Physical Society.

[9]  Susanne Still,et al.  Physical limitations of work extraction from temporal correlations. , 2019, Physical review. E.

[10]  I. Prigogine.  Chemical Kinetics and Dynamics , 2003, Annals of the New York Academy of Sciences.

[11]  E. Lutz,et al.  Nonequilibrium entropy production for open quantum systems. , 2011, Physical review letters.

[12]  Milburn,et al.  Quantum optical Fredkin gate. , 1989, Physical review letters.

[13]  Keiji Saito,et al.  Thermodynamic Bounds on Precision in Ballistic Multiterminal Transport. , 2017, Physical review letters.

[14]  Christopher Jarzynski,et al.  Stochastic and Macroscopic Thermodynamics of Strongly Coupled Systems , 2017 .

[15]  R. Kubo.  Statistical Physics II: Nonequilibrium Statistical Mechanics , 2003 .

[16]  Todd R. Gingrich,et al.  Proof of the finite-time thermodynamic uncertainty relation for steady-state currents. , 2017, Physical review. E.

[17]  沙川 貴大,et al.  Thermodynamics of information processing in small systems , 2011 .

[18]  U. Seifert.  From Stochastic Thermodynamics to Thermodynamic Inference , 2019, Annual Review of Condensed Matter Physics.

[19]  J. Crutchfield,et al.  Fluctuations When Driving Between Nonequilibrium Steady States , 2016, 1610.09444.

[20]  James P. Crutchfield,et al.  Balancing Error and Dissipation in Computing , 2019 .

[21]  Robert Alicki,et al.  The quantum open system as a model of the heat engine , 1979 .

[22]  James P. Crutchfield,et al.  Functional Thermodynamics of Maxwellian Ratchets: Constructing and Deconstructing Patterns, Randomizing and Derandomizing Behaviors , 2020 .

[23]  Tommaso Toffoli,et al.  A nanomechanical Fredkin gate. , 2014, Nano letters.

[24]  U. Seifert,et al.  Operationally Accessible Bounds on Fluctuations and Entropy Production in Periodically Driven Systems. , 2019, Physical review letters.

[25]  Patrick S. Stumpf,et al.  Stem Cell Differentiation as a Non-Markov Stochastic Process , 2017, Cell systems.

[26]  A. B. Boyd,et al.  Identifying functional thermodynamics in autonomous Maxwellian ratchets , 2015, 1507.01537.

[27]  Hidden Markov models for stochastic thermodynamics , 2015 .

[28]  Christian Van Den Broeck,et al.  Stochastic thermodynamics: A brief introduction , 2013 .

[29]  James P. Crutchfield,et al.  Transient Dissipation and Structural Costs of Physical Information Transduction , 2017, Physical review letters.

[30]  Massimiliano Esposito,et al.  Ensemble and trajectory thermodynamics: A brief introduction , 2014, 1403.1777.

[31]  James P. Crutchfield,et al.  Above and Beyond the Landauer Bound: Thermodynamics of Modularity , 2017, Physical Review X.

[32]  L. Ferialdi.  Exact Closed Master Equation for Gaussian Non-Markovian Dynamics. , 2015, Physical review letters.

[33]  C. Maes.  Frenetic Bounds on the Entropy Production. , 2017, Physical review letters.

[34]  K. Laidler.  The development of the Arrhenius equation , 1984 .