Ladyman, James and Presnell, Stuart and Short, Anthony J. and Groisman, Berry (2006) The Connection between Logical and Thermodynamic Irreversibility. [Preprint]

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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 kTln2 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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Item Type:	Preprint
Creators:	Creators Email ORCID Ladyman, James Presnell, Stuart Short, Anthony J. Groisman, Berry
Keywords:	Landauer's principle, Irreversibility, Thermodynamics, Computation
Subjects:	Specific Sciences > Computer Science Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User:	Anthony John Short
Date Deposited:	26 Mar 2006
Last Modified:	07 Oct 2010 15:14
Item ID:	2689
Subjects:	Specific Sciences > Computer Science Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date:	March 2006
URI:	https://philsci-archive.pitt.edu/id/eprint/2689

Available Versions of this Item

• The Connection between Logical and Thermodynamical Irreversibility. (deposited 22 Jul 2005)
  • The Connection between Logical and Thermodynamic Irreversibility. (deposited 26 Mar 2006) [Currently Displayed]

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