Abstract
Information processing typically occurs via the composition of modular units, such as the universal logic gates found in discrete computation circuits. The benefit of modular information processing, in contrast to globally integrated information processing, is that complex computations are more easily and flexibly implemented via a series of simpler, localized information processing operations that 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 bound on the work required to erase information. Localized operations are unable to leverage global correlations, which 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 a computational task modularly, measuring a structural energy cost. It determines the thermodynamic efficiency of different modular implementations of the same computation, and so it has immediate consequences for the architecture of physically embedded transducers, known as information ratchets. Constructively, we show how to circumvent modularity dissipation by designing internal ratchet states that capture the information reservoir’s global correlations and patterns. Thus, there are routes to thermodynamic efficiency that circumvent globally integrated protocols and instead reduce modularity dissipation to optimize the architecture of computations composed of a series of localized operations.
- Received 15 August 2017
- Revised 9 April 2018
DOI:https://doi.org/10.1103/PhysRevX.8.031036
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
In 1961, physicist Rolf Landauer famously showed that erasing information requires work, regardless of how it is done. This link between logic and energy has guided the thermodynamics of information processing for decades. Modern computation is always broken up into many simpler modular components, for ease and flexibility of design. Biological evolution, too, has taken advantage of modularity—from cells to organs, one finds compartmentalization. However, we have discovered that modularity introduces an additional, irretrievable energy cost.
We developed a mathematical model of information processing that takes into account the thermodynamic impact on breaking a computation into multiple steps. This “modularity dissipation” quantifies the thermodynamic efficiency of different implementations of the same computation. For systems that leverage informational resources in their environment, we show that thermodynamically efficient information engines must store all predictable information about their inputs, requisitely matching the structural complexity of their environment.
One positive benefit is that, while modular computations potentially cost more than predicted by Landauer erasure, it is possible to avoid additional dissipation by properly designing a computation to store global correlations.
