Speed limit for a highly irreversible process and tight finite-time Landauer's bound

TL;DR

This paper derives a precise finite-time Landauer's bound that quantifies the minimal energetic cost of information erasure during rapid, highly irreversible processes, revealing increased heat dissipation in such scenarios.

Contribution

It establishes a tight finite-time Landauer's bound based on a general classical speed limit, capturing divergence in energetic costs for highly irreversible processes.

Findings

The bound accurately predicts divergent costs in highly irreversible processes.

An optimal dynamics saturating the bound is identified.

Validation through discrete and coarse-grained bit systems confirms the theoretical predictions.

Abstract

Landauer's bound is the minimum thermodynamic cost for erasing one bit of information. As this bound is achievable only for quasistatic processes, finite-time operation incurs additional energetic costs. We find a tight finite-time Landauer's bound by establishing a general form of the classical speed limit. This tight bound well captures the divergent behavior associated with the additional cost of a highly irreversible process, which scales differently from a nearly irreversible process. We also find an optimal dynamics which saturates the equality of the bound. We demonstrate the validity of this bound via discrete one-bit and coarse-grained bit systems. Our work implies that more heat dissipation than expected occurs during high-speed irreversible computation.