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Thermodynamics of stochastic Turing machines
Philipp Strasberg1, Javier Cerrillo1, Gernot Schaller1
1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
Researchers developed stochastic models mirroring Turing machine computations, offering a thermodynamic interpretation of computing. These models demonstrate that while steady-state entropy production can be minimized, total entropy production scales logarithmically with computational steps.
Area of Science:
- * Physics
- * Computer Science
- * Thermodynamics
Background:
- * Stochastic models offer a framework for understanding computational processes.
- * The thermodynamic interpretation of computation is a key area of research.
- * Brownian computers provide an analogy for stochastic computational systems.
Purpose of the Study:
- * To construct stochastic models that simulate a general-purpose computer (Turing machine).
- * To investigate the thermodynamic properties of these computational models.
- * To analyze entropy production in both stationary and dynamic regimes.
Main Methods:
- * Development of discrete state systems obeying a Markovian master equation.
- * Logical reversibility and thermodynamic consistency were enforced in the models.
- * Approximation of the master equation by a Fokker-Planck equation in the stationary regime.
Main Results:
- * Stochastic models successfully mimic Turing machine behavior.
- * The master equation describes a one-step process on a large state space.
- * Entropy production rate at steady state can be made arbitrarily small.
- * Total entropy production is finite and grows logarithmically with computational steps.
Conclusions:
- * Logically reversible stochastic models provide a valid framework for studying the thermodynamics of computation.
- * The study offers insights into the fundamental limits of energy dissipation in computing.
- * Findings suggest a trade-off between minimizing instantaneous entropy production and the cumulative cost of computation.
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