Above and Beyond the Landauer Bound: Thermodynamics of Modularity

Abstract

Information processing typically occurs via the composition of modular units, such as universal logic gates. The benefit of modular information processing, in contrast to globally integrated information processing, is that complex global computations are more easily and flexibly implemented via a series of simpler, localized information processing operations which only control and change local degrees of freedom. We show that, despite these benefits, there are unavoidable thermodynamic costs to modularity---costs that arise directly from the operation of localized processing and that go beyond Landauer's dissipation bound for erasing information. Integrated computations can achieve Landauer's bound, however, when they globally coordinate the control of all of an information reservoir's degrees of freedom. Unfortunately, global correlations among the information-bearing degrees of freedom are easily lost by modular implementations. This is costly since such correlations are a thermodynamic fuel. We quantify the minimum irretrievable dissipation of modular computations in terms of the difference between the change in global nonequilibrium free energy, which captures these global correlations, and the local (marginal) change in nonequilibrium free energy, which bounds modular work production. This modularity dissipation is proportional to the amount of additional work required to perform the computational task modularly. It has immediate consequences for physically embedded transducers, known as information ratchets. We show how to circumvent modularity dissipation by designing internal ratchet states that capture the global correlations and patterns in the ratchet's information reservoir. Designed in this way, information ratchets match the optimum thermodynamic efficiency of globally integrated computations.

17 pages, 9 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/idolip.htm

References in corpus (10)

• High-precision test of Landauer's principle in a feedback trap
• Work and information processing in a solvable model of Maxwell's demon
• The thermodynamics of prediction
• Basins of attraction of a nonlinear nanomechanical resonator
• Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence
• Emergence of order from turbulence in an isolated planar superfluid
• Quantum thermodynamics with local control
• Transient Dissipation and Structural Costs of Physical Information Transduction
• Thermodynamics of Random Number Generation
• Relations Between Work and Entropy Production for General Information-Driven, Finite-State Engines

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