Landauer's erasure principle in non-equilibrium systems

TL;DR

This paper compares two generalizations of Landauer's erasure principle, showing that Maroney's version applies to non-equilibrium states while Turgut's does not, and clarifies their implications for thermodynamic reversibility.

Contribution

It demonstrates the limitations of Turgut's generalization in non-equilibrium systems and establishes the robustness of Maroney's inequality in such contexts.

Findings

Turgut's inequality does not hold for non-equilibrium states.

Maroney's inequality remains valid in non-equilibrium conditions.

Maroney's inequality provides necessary and sufficient conditions for reversibility.

Abstract

In two recent papers, Maroney and Turgut separately and independently show generalisations of Landauer's erasure principle to indeterministic logical operations, as well as to logical states with variable energies and entropies. Here we show that, although Turgut's generalisation seems more powerful, in that it implies but is not implied by Maroney's and that it does not rely upon initial probability distributions over logical states, it does not hold for non-equilibrium states, while Maroney's generalisation holds even in non-equilibrium. While a generalisation of Turgut's inequality to non-equilibrium seems possible, it lacks the properties that makes the equilibrium inequality appealing. The non-equilibrium generalisation also no longer implies Maroney's inequality, which may still be derived independently. Furthermore, we show that Turgut's inequality can only give a necessary, but not sufficient, criteria for thermodynamic reversibility. Maroney's inequality gives the necessary and sufficient conditions.