The connection between logical and thermodynamic 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 1 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.

Information Equation of State

“…Landauer's principle is fully compatible with the laws of thermodynamics [9], [11][12][13][14]. Indeed Landauer's principle has been used to reconcile the operation of Maxwell's Demon with the second law of thermodynamics.…”

Landauer defended: Reply to Norton

“…It also exposed deficiencies in the extant discussions of LP in the wider literature, demonstrated that LP could not be established by reasoning about particular cases, and showed that a general proof of LP had not been given. Ladyman et al (2007), hereafter LPSG, proposed a model of the implementation of logical operations by physical processes in order to clarify the exact statement of LP, and then offered a new proof of the latter based on the construction of a thermodynamic cycle, arguing that if LP were false it would be possible to harness a machine that violated it to produce a violation of the second law of thermodynamics. In a recent paper in this journal (2011), John Norton directly challenges the consistency of that proof.…”

All Shook Up: Fluctuations, Maxwell’s Demon and the Thermodynamics of Computation

“…It is no small undertaking, since a change to the fundamental law must be propagated consistently through all of thermodynamics. See Ladyman et al [30,31]. The challenge is a worthy one and they have made a quite creditable effort.…”

“…For completeness, from (32) and (28), the thermodynamic entropy created in the case of the 5 g bead for n = 10 is k(n − 1)m(2.3026) = 62.2 k. From (30), the thermodynamic entropy created in the release of the 100 amu bead for n = 10 is k ln 9 = 2.197 k. The first entropy creation is significantly larger since the process recompresses the bead location to the final state, by a less efficient means.…”