The work value of information

TL;DR

This paper establishes quantitative relations between work and information, viewing work extraction as a game influenced by knowledge and risk, and connects thermodynamics with information theory through simple, universal formulas.

Contribution

It introduces a unified framework linking work extraction to information and risk, extending thermodynamics to finite and correlated systems using the smooth entropy approach.

Findings

Derived simple formulas for maximum work extraction under different risk tolerances.

Connected heat engine concepts with the smooth entropy framework.

Extended thermodynamic principles to finite and correlated systems.

Abstract

We present quantitative relations between work and information that are valid both for finite sized and internally correlated systems as well in the thermodynamical limit. We suggest work extraction should be viewed as a game where the amount of work an agent can extract depends on how well it can guess the micro-state of the system. In general it depends both on the agent's knowledge and risk-tolerance, because the agent can bet on facts that are not certain and thereby risk failure of the work extraction. We derive strikingly simple expressions for the extractable work in the extreme cases of effectively zero- and arbitrary risk tolerance respectively, thereby enveloping all cases. Our derivation makes a connection between heat engines and the smooth entropy approach. The latter has recently extended Shannon theory to encompass finite sized and internally correlated bit strings, and our analysis points the way to an analogous extension of statistical mechanics.