Landauer defended: Reply to Norton

Abstract

Ladyman et al (2007) proposed a model of the implementation of logical operations by physical processes in order to clarify the exact statement of Landauer's Principle, and then offered a new proof of the latter based on the construction of a thermodynamic cycle, arguing that if Landauer's Principle 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, John Norton (2011) directly challenges the consistency of that proof. In the present paper we defend the proof given by Ladyman et al against his critique.In particular, contrary to what Norton claims, we argue that the processes used in the proof cannot be used to construct a cycle that enacts erasure in a thermodynamically reversible way, and that he does not show that the processes used in the proof violate the Second Law of Thermodynamics.

Entropy and Computation: The Landauer-Bennett Thesis Reexamined

“…A defense of Landauer's thesis is in e.g. Bub [13] and Ladyman and Robertson [14].) To see this, consider first Figures 7 and 8, which illustrate the necessary and sufficient condition for erasure that we call blending.…”

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

“…(Note that this conclusion cannot derive directly from the Clausius definition that S = q rev /T since the process is not a thermodynamically reversible process.) We can relate this entropy creation to the odds ratio O fin by combining (28) and (31) to recover: (32) where the last approximation holds for P fin close to unity.…”

“…The assumption of the inaccessibility of these intermediate stages enabled us to pass from the relation (22) on P fin and P init to the minimum entropy relation (23). For the bead on the inclined wire, the n−2 intermediate stages are all accessible and their accessibility is responsible for the factor of (n − 1) in (32).…”

“…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.…”

Going Round in Circles: Landauer vs. Norton on the Thermodynamics of Computation

“…Norton [12] argued that the physical processes used by LPSG in their proof allow for violations of SL, and can used to construct a counterexample to LP, and thus that the proof fails. However, Ladyman and Robertson [13] showed that this criticism was based on an illicit conception of controlled operations, and violation of the correct analysis of implementation. However, Norton's latest criticism of LP is not confined to LSPG's proof, and in [14,15], he offers a no go result that he purports to be the end of the thermodynamics of computation.…”