An improved Landauer Principle with finite-size corrections

TL;DR

This paper presents a rigorous, quantum-mechanics-based formulation of Landauer's Principle, providing an equality version that includes finite-size corrections depending on the reservoir's size, thus refining the traditional bound.

Contribution

It introduces an improved, equality-based Landauer's Principle with explicit finite-size corrections derived from quantum statistical mechanics.

Findings

Provides a rigorous proof of an equality form of Landauer's Principle.

Derives explicit finite-size corrections to the traditional Landauer bound.

Shows corrections depend on the effective size of the thermal reservoir.

Abstract

Landauer's Principle relates entropy decrease and heat dissipation during logically irreversible processes. Most theoretical justifications of Landauer's Principle either use thermodynamic reasoning or rely on specific models based on arguable assumptions. Here, we aim at a general and minimal setup to formulate Landauer's Principle in precise terms. We provide a simple and rigorous proof of an improved version of the Principle, which is formulated in terms of an equality rather than an inequality. The proof is based on quantum statistical mechanics concepts rather than on thermodynamic argumentation. From this equality version, we obtain explicit improvements of Landauer's bound that depend on the effective size of the thermal reservoir and reduce to Landauer's bound only for infinite-sized reservoirs.