Thermodynamics of Prediction

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Thermodynamics of Prediction

Susanne Still, David A. Sivak, Anthony J. Bell, and Gavin E. Crooks

Phys. Rev. Lett. 109, 120604 – Published 19 September 2012

Abstract

A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system’s state retains information about past environmental fluctuations, and a fraction of this information is predictive of future ones. The remaining nonpredictive information reflects model complexity that does not improve predictive power, and thus represents the ineffectiveness of the model. We expose the fundamental equivalence between this model inefficiency and thermodynamic inefficiency, measured by dissipation. Our results hold arbitrarily far from thermodynamic equilibrium and are applicable to a wide range of systems, including biomolecular machines. They highlight a profound connection between the effective use of information and efficient thermodynamic operation: any system constructed to keep memory about its environment and to operate with maximal energetic efficiency has to be predictive.

Received 15 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.120604

Authors & Affiliations

Susanne Still^1,*, David A. Sivak^2,†, Anthony J. Bell³, and Gavin E. Crooks²

¹University of Hawaii at Mānoa, Information and Computer Sciences, Honolulu, Hawaii 96822, USA
²Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Redwood Center for Theoretical Neuroscience, University of California, Berkeley, California 94720, USA

^*sstill@hawaii.edu
^†Present address: Center for Systems and Synthetic Biology, University of California, San Francisco, California 94158, USA.