The Minimal Work Cost of Information Processing

TL;DR

This paper derives a precise formula for the minimal thermodynamic work needed for any logical information process, linking information entropy with thermodynamic costs and accounting for fluctuations.

Contribution

It provides an exact expression for the minimal work cost of logical processes, incorporating statistical fluctuations and connecting thermodynamics with information theory.

Findings

The minimal work cost equals the entropy of discarded information conditioned on the output.

The formula applies to practical scenarios like circuits and quantum measurements.

It clarifies the thermodynamic role of information entropy in computation.

Abstract

Irreversible information processing cannot be carried out without some inevitable thermodynamical work cost. This fundamental restriction, known as Landauer's principle, is increasingly relevant today, as the energy dissipation of computing devices impedes the development of their performance. Here we determine the minimal work required to carry out any logical process, for instance a computation. It is given by the entropy of the discarded information conditional to the output of the computation. Our formula takes precisely into account the statistically fluctuating work requirement of the logical process. It enables the explicit calculation of practical scenarios, such as computational circuits or quantum measurements. On the conceptual level, our result gives a precise and operationally justified connection between thermodynamic and information entropy, and explains the emergence of the entropy state function in macroscopic thermodynamics.