Thermodynamics of complexity and pattern manipulation

Andrew J. P. Garner, Jayne Thompson, Vlatko Vedral, and Mile Gu
Phys. Rev. E 95, 042140 – Published 24 April 2017

Abstract

Many organisms capitalize on their ability to predict the environment to maximize available free energy and reinvest this energy to create new complex structures. This functionality relies on the manipulation of patterns—temporally ordered sequences of data. Here, we propose a framework to describe pattern manipulators—devices that convert thermodynamic work to patterns or vice versa—and use them to build a “pattern engine” that facilitates a thermodynamic cycle of pattern creation and consumption. We show that the least heat dissipation is achieved by the provably simplest devices, the ones that exhibit desired operational behavior while maintaining the least internal memory. We derive the ultimate limits of this heat dissipation and show that it is generally nonzero and connected with the pattern's intrinsic crypticity—a complexity theoretic quantity that captures the puzzling difference between the amount of information the pattern's past behavior reveals about its future and the amount one needs to communicate about this past to optimally predict the future.

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  • Received 10 October 2016
  • Revised 30 November 2016

DOI:https://doi.org/10.1103/PhysRevE.95.042140

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Andrew J. P. Garner1,2,*, Jayne Thompson1, Vlatko Vedral3,1,4,2, and Mile Gu5,6,1,2,†

  • 1Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
  • 2Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
  • 3Atomic and Laser Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
  • 4Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117543
  • 5School of Physical and Mathematical Sciences, Nanyang Technological University, 639673, Singapore
  • 6Complexity Institute, Nanyang Technological University, 639673, Singapore

  • *ajpgarner@nus.edu.sg
  • cqtmileg@nus.edu.sg

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Issue

Vol. 95, Iss. 4 — April 2017

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