Above and Beyond the Landauer Bound: Thermodynamics of Modularity

TL;DR

This paper investigates the thermodynamic costs of modular information processing, revealing unavoidable dissipation beyond Landauer's bound and proposing designs to minimize this dissipation by capturing global correlations.

Contribution

It quantifies the minimum irretrievable dissipation in modular computations and introduces design principles for information ratchets to achieve global optimal efficiency.

Findings

Modular computations incur additional thermodynamic costs due to loss of global correlations.

Global coordination can achieve Landauer's bound, but modularity introduces dissipation.

Designing internal ratchet states can recover correlations and match optimal thermodynamic efficiency.

Abstract

Information processing typically occurs via the composition of modular units, such as universal logic gates. The benefit of modular information processing, in contrast to globally integrated information processing, is that complex global computations are more easily and flexibly implemented via a series of simpler, localized information processing operations which only control and change local degrees of freedom. We show that, despite these benefits, there are unavoidable thermodynamic costs to modularity---costs that arise directly from the operation of localized processing and that go beyond Landauer's dissipation bound for erasing information. Integrated computations can achieve Landauer's bound, however, when they globally coordinate the control of all of an information reservoir's degrees of freedom. Unfortunately, global correlations among the information-bearing degrees of freedom are easily lost by modular implementations. This is costly since such correlations are a thermodynamic fuel. We quantify the minimum irretrievable dissipation of modular computations in terms of the difference between the change in global nonequilibrium free energy, which captures these global correlations, and the local (marginal) change in nonequilibrium free energy, which bounds modular work production. This modularity dissipation is proportional to the amount of additional work required to perform the computational task modularly. It has immediate consequences for physically embedded transducers, known as information ratchets. We show how to circumvent modularity dissipation by designing internal ratchet states that capture the global correlations and patterns in the ratchet's information reservoir. Designed in this way, information ratchets match the optimum thermodynamic efficiency of globally integrated computations.