TY - JOUR

T1 - The physics of implementing logic

T2 - Landauer's principle and the multiple-computations theorem

AU - Hemmo, Meir

AU - Shenker, Orly

N1 - Publisher Copyright:
© 2019 Elsevier Ltd

PY - 2019/11

Y1 - 2019/11

N2 - 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.

AB - 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.

KW - Entropy

KW - Individuation of computation

KW - Landauer's principle

KW - Logical (ir)reversibility

KW - Second law of thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=85071357262&partnerID=8YFLogxK

U2 - 10.1016/j.shpsb.2019.07.001

DO - 10.1016/j.shpsb.2019.07.001

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AN - SCOPUS:85071357262

SN - 1355-2198

VL - 68

SP - 90

EP - 105

JO - Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

JF - Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

ER -