2015/06/02 by Philipp Strasberg, Javier Cerrillo, Gernot Schaller +1 · 1 voice · 36 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Mathematical economics #Mathematics #Physics #Programming language #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Statistical physics #Thermodynamics #Turing machine #cond-mat.stat-mech #cs.FL
paper · pdf · doi:10.1103/physreve.92.042104
published in Physical Review E 92(4), 042104 (American Physical Society) · 13 pages incl. appendix, 3 figures and 1 table, slightly changed version as published in PRE
openalex publication_date 2015/10/05 · arxiv created 2015/10/12 · arxiv updated 2015/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.