Balancing Error and Dissipation in Computing

TL;DR

This paper reveals a fundamental tradeoff between error probability and energy dissipation in reliable digital computing, emphasizing the importance of time-asymmetry for thermodynamic efficiency.

Contribution

It demonstrates that time-symmetric control imposes a fundamental error-energy-efficiency tradeoff, surpassing the Landauer limit and highlighting the role of time-asymmetry in efficient computation.

Findings

Error probability diverges logarithmically with energy in nonreciprocal transitions.

Reciprocity is a stricter condition for thermodynamic efficiency than logical reversibility.

Biological information processing also faces a similar error-dissipation tradeoff.

Abstract

Modern digital electronics support remarkably reliable computing, especially given the challenge of controlling nanoscale logical components that interact in fluctuating environments. However, we demonstrate that the high-reliability limit is subject to a fundamental error-energy-efficiency tradeoff that arises from time-symmetric control: Requiring a low probability of error causes energy consumption to diverge as logarithm of the inverse error rate for nonreciprocal logical transitions. The reciprocity (self-invertibility) of a computation is a stricter condition for thermodynamic efficiency than logical reversibility (invertibility), the latter being the root of Landauer's work bound on erasing information. Beyond engineered computation, the results identify a generic error-dissipation tradeoff in steady-state transformations of genetic information carried out by biological organisms. The lesson is that computation under time-symmetric control cannot reach, and is often far above, the Landauer limit. In this way, time-asymmetry becomes a design principle for thermodynamically efficient computing.