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Landauer's bound is the minimum thermodynamic cost for erasing one bit ofinformation. As this bound is achievable only for quasistatic processes,finite-time operation incurs additional energetic costs. We find a tightfinite-time Landauer's bound by establishing a general form of the classicalspeed limit. This tight bound well captures the divergent behavior associatedwith the additional cost of a highly irreversible process, which scalesdifferently from a nearly irreversible process. We also find an optimaldynamics which saturates the equality of the bound. We demonstrate the validityof this bound via discrete one-bit and coarse-grained bit systems. Our workimplies that more heat dissipation than expected occurs during high-speedirreversible computation.

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