The physics of implementing logic: Landauer's principle and the multiple-computations theorem

Meir Hemmo, Orly Shenker

Research output: Contribution to journalArticlepeer-review

Abstract

This paper makes a novel linkage between the multiple-computations theorem in philosophy of mind and Landauer's principle in physics. The multiple-computations theorem implies that certain physical systems implement simultaneously more than one computation. Landauer's principle implies that the physical implementation of “logically irreversible” functions is accompanied by minimal entropy increase. We show that the multiple-computations theorem is incompatible with, or at least challenges, the universal validity of Landauer's principle. To this end we provide accounts of both ideas in terms of low-level fundamental concepts in statistical mechanics, thus providing a deeper understanding of these ideas than their standard formulations given in the high-level terms of thermodynamics and cognitive science. Since Landauer's principle is pivotal in the attempts to derive the universal validity of the second law of thermodynamics in statistical mechanics, our result entails that the multiple-computations theorem has crucial implications with respect to the second law. Finally, our analysis contributes to the understanding of notions, such as “logical irreversibility,” “entropy increase,” “implementing a computation,” in terms of fundamental physics, and to resolving open questions in the literature of both fields, such as: what could it possibly mean that a certain physical process implements a certain computation.

Original languageEnglish
Pages (from-to)90-105
Number of pages16
JournalStudies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
Volume68
DOIs
StatePublished - Nov 2019

Bibliographical note

Funding Information:
This research was supported by the Israel Science Foundation ( ISF ), grant number: 1148/18 and by a grant from Lockheed-Martin.

Funding Information:
We thank: Eli Drezner, Nir Fresco, James Ladyman, and Oron Shagrir for valuable comments on earlier drafts of this paper; Erez Firt, Violetta Rosemberg, Aviv Spector and Gal Vishne from our ISF research group, for discussions; and an anonymous reviewer, for raising helpful points and questions. We thank the Israel Science Foundation and Lockheed-Martin for supporting this research.

Publisher Copyright:
© 2019 Elsevier Ltd

Keywords

  • Entropy
  • Individuation of computation
  • Landauer's principle
  • Logical (ir)reversibility
  • Second law of thermodynamics

ASJC Scopus subject areas

  • History
  • Physics and Astronomy (all)
  • History and Philosophy of Science

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