The thermodynamic cost of reliability and low temperatures: Tightening Landauer's principle and the Second Law

TL;DR

This paper refines Landauer's principle by linking the reliability of information erasure and cooling to the statistical distinguishability of resource states from equilibrium, emphasizing the role of relative information.

Contribution

It introduces a framework connecting thermodynamic worth to the statistical distinguishability of resource states, providing tighter bounds on reliability and energy costs.

Findings

Reliability bounds are determined by the relative information of resource states.

Kullback-Leibler divergence quantifies the resource's thermodynamic worth.

Asymmetry of relative information affects the bounds on erasure and cooling.

Abstract

Landauer's principle states that the erasure of one bit of information requires the free energy kT ln 2. We argue that the reliability of the bit erasure process is bounded by the accuracy inherent in the statistical state of the energy source (`the resources') driving the process. We develop a general framework describing the `thermodynamic worth' of the resources with respect to reliable bit erasure or good cooling. This worth turns out to be given by the distinguishability of the resource's state from its equilibrium state in the sense of a statistical inference problem. Accordingly, Kullback-Leibler relative information is a decisive quantity for the `worth' of the resource's state. Due to the asymmetry of relative information, the reliability of the erasure process is bounded rather by the relative information of the equilibrium state wit respect to the actual state than by the relative information of the actual state with respect to the equilibrium state (which is the free energy up to constants).