Speed Limit for a Highly Irreversible Process and Tight Finite-Time Landauer’s Bound

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 Letter implies that more heat dissipation than expected occurs during high-speed irreversible computation.

Figure 1

(a) and (b) Schematics of the two erasure models: discrete one-bit system (a) and coarse-grained bit system (b). (c) Plot of $\mathrm{\Sigma }/\ell$ versus $v^{-1}$ for discrete system (gray cross) and continuous system (green circle). The orange solid (sky-blue dashed) curve denotes the Pinsker (symmetric KLD) bound. The result of the optimal protocol is denoted by a red dot circle. (d) Plot of $\mathrm{\Sigma }$ divided by the symmetric KLD bound $B_S$ versus $v^{-1}$. For a fixed $\ell$ and $A(t)$, $v^{-1}$ can be simply regarded as a scaled time. The same data are used for (c) and (d).