Quantum Mpemba Speedups in the Thermodynamics of Landauer Erasure

Landauer's principle dictates that any logically irreversible bit erasure dissipates a minimum amount of heat in the quasistatic limit. However, realistic devices operate in finite time, incurring excess thermodynamic costs from nonequilibrium relaxation. This paper investigates whether nonequilibrium quantum initial states—specifically those exhibiting quantum Mpemba-like behavior—can be harnessed to reduce finite-time erasure times and suppress heat dissipation below standard expectations.

The study considers a finite-dimensional quantum memory coupled to a thermal reservoir via a Davies-type Lindblad generator. The memory is initialized in a thermal state of an input Hamiltonian at a tunable preparation temperature, then instantaneously quenched to an erasure Hamiltonian. The subsequent dissipative evolution is analyzed through the spectral decomposition of the Liouvillian superoperator. By tracking biorthogonal right and left eigenmodes, the authors isolate the slowest relaxation mode and derive modified finite-time bounds for both the operational erasure time and the associated heat dissipation.

Using a minimal qutrit model where an excited doublet is coherently coupled, the author demonstrates that a hotter initial preparation can have a smaller projection onto the slowest Liouvillian relaxation mode than a colder preparation. Under this condition, the hotter state bypasses the slowest dynamical channel, reaching the target erasure fidelity faster. Furthermore, the author proves a general theorem showing that when the slow-mode overlap is appropriately suppressed, the integrated entropy production decreases, leading to a genuine reduction in the total heat discharged into the thermal bath.