The connection between logical and thermodynamical irreversibility

Abstract

There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: The erasure of one bit of information in a computational device is necessarily accompanied by a generation of kT ln 2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. John Norton (2005) and Owen Maroney (2005) both argue that Landauer's Principle has not been shown to hold in general, and Maroney offers a method that he claims instantiates the operation reset in a thermodynamically reversible way. In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences (assuming the second law of thermodynamics). We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation 'reset', and thereby recover the quantitative form of Landauer's Principle.

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Author Profiles

Tony Short
University of Bristol
James Ladyman
University of Bristol
Stuart Presnell
University of Bristol

Citations of this work

Compendium of the Foundations of Classical Statistical Physics.Jos Uffink - 2005 - In Jeremy Butterfield & John Earman (eds.), Handbook of the Philosophy of Physics. Elsevier.
The Use of the Information-Theoretic Entropy in Thermodynamics.James Ladyman, Stuart Presnell & Anthony J. Short - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2):315-324.
Does a Computer Have an Arrow of Time?Owen J. E. Maroney - 2010 - Foundations of Physics 40 (2):205-238.

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References found in this work

Bluff Your Way in the Second Law of Thermodynamics.Jos Uffink - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (3):305-394.
Eaters of the Lotus: Landauer's Principle and the Return of Maxwell's Demon.John D. Norton - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2):375-411.
Notes on Landauer's Principle, Reversible Computation, and Maxwell's Demon.Charles H. Bennett - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):501-510.
Notes on Landauer's Principle, Reversible Computation, and Maxwell's Demon.Charles H. Bennett - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):501-510.
The (Absence of a) Relationship Between Thermodynamic and Logical Reversibility.O. J. E. Maroney - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2):355-374.

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