Thermodynamics of stochastic Turing machines

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 cons...

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Detalles Bibliográficos
Autores: Strasberg, Philipp, Cerrillo Moreno, Javier, Schaller, Gernot, Brandes, Tobias
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Institución:Universidad Politécnica de Cartagena(UPCT)
Repositorio:Repositorio Digital UPCT
OAI Identifier:oai:repositorio.upct.es:10317/13374
Acceso en línea:http://hdl.handle.net/10317/13374
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.042104
Access Level:acceso abierto
Palabra clave:stochastic models
general-purpose computer
Turing machine
Markovian master equation
thermodynamic interpretation
Fokker-Planck equation
Física Aplicada
Descripción
Sumario: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.