Thermodynamics of stochastic Turing machines

Journal ar
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
  • Volumen: 92
  • Número: 4
  • Fecha: 05 October 2015
  • ISSN: 15502376 15393755
  • Source Type: Journal
  • DOI: 10.1103/PhysRevE.92.042104
  • Document Type: Article
  • Publisher: American Physical
© 2015 American Physical Society.In analogy to Brownian computers we explicitly show how to construct stochastic models which mimic the behavior of a general-purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps.

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