Transfer entropy in physical systems and the arrow of time

Richard E. Spinney, Joseph T. Lizier, and Mikhail Prokopenko
Phys. Rev. E 94, 022135 – Published 24 August 2016

Abstract

Recent developments have cemented the realization that many concepts and quantities in thermodynamics and information theory are shared. In this paper, we consider a highly relevant quantity in information theory and complex systems, the transfer entropy, and explore its thermodynamic role by considering the implications of time reversal upon it. By doing so we highlight the role of information dynamics on the nuanced question of observer perspective within thermodynamics by relating the temporal irreversibility in the information dynamics to the configurational (or spatial) resolution of the thermodynamics. We then highlight its role in perhaps the most enduring paradox in modern physics, the manifestation of a (thermodynamic) arrow of time. We find that for systems that process information such as those undergoing feedback, a robust arrow of time can be formulated by considering both the apparent physical behavior which leads to conventional entropy production and the information dynamics which leads to a quantity we call the information theoretic arrow of time. We also offer an interpretation in terms of optimal encoding of observed physical behavior.

  • Figure
  • Received 13 April 2016

DOI:https://doi.org/10.1103/PhysRevE.94.022135

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Richard E. Spinney, Joseph T. Lizier, and Mikhail Prokopenko

  • Centre for Complex Systems, The University of Sydney, Sydney, New South Wales, Australia, 2006

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Issue

Vol. 94, Iss. 2 — August 2016

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