Shortcuts to Thermodynamic Computing: The Cost of Fast and Faithful Erasure

TL;DR

This paper explores the energetic costs and physical limits of finite-time information erasure, demonstrating how shortcuts can speed up processes at the expense of additional dissipation, and analyzing factors influencing work requirements.

Contribution

It introduces a method to design finite-time shortcuts for thermodynamic computations, quantifies the dissipated work, and examines how storage robustness impacts erasure costs.

Findings

Shortcuts enable rapid, accurate computation with finite work.

Dissipated work scales with computation rate and system size.

Perfect erasure can be achieved in finite time with finite work.

Abstract

Landauer's Principle states that the energy cost of information processing must exceed the product of the temperature and the change in Shannon entropy of the information-bearing degrees of freedom. However, this lower bound is achievable only for quasistatic, near-equilibrium computations -- that is, only over infinite time. In practice, information processing takes place in finite time, resulting in dissipation and potentially unreliable logical outcomes. For overdamped Langevin dynamics, we show that counterdiabatic potentials can be crafted to guide systems rapidly and accurately along desired computational paths, providing shortcuts that allows for the precise design of finite-time computations. Such shortcuts require additional work, beyond Landauer's bound, that is irretrievably dissipated into the environment. We show that this dissipated work is proportional to the computation rate as well as the square of the information-storing system's length scale. As a paradigmatic example, we design shortcuts to erase a bit of information metastably stored in a double-well potential. Though dissipated work generally increases with erasure fidelity, we show that it is possible perform perfect erasure in finite time with finite work. We also show that the robustness of information storage affects the energetic cost of erasure---specifically, the dissipated work scales as the information lifetime of the bistable system. Our analysis exposes a rich and nuanced relationship between work, speed, size of the information-bearing degrees of freedom, storage robustness, and the difference between initial and final informational statistics.