The thermodynamics of the quantum Mpemba effect
arxiv(2024)
摘要
We investigate the quantum Mpemba effect from the perspective of
non-equilibrium quantum thermodynamics by studying relaxation dynamics
described by Davies maps. Starting from a state with coherences in the energy
eigenbasis, we demonstrate that an exponential speedup to equilibrium will
always occur if the state is transformed to a diagonal state in the energy
eigenbasis, provided that the spectral gap of the generator is defined by a
complex eigenvalue. When the transformed state has a higher non-equilibrium
free energy, we argue using thermodynamic reasoning that this is a
genuine quantum Mpemba effect. Furthermore, we show how a unitary
transformation on an initial state can always be constructed to yield the
effect and demonstrate our findings by studying the dynamics of both the
non-equilibrium free energy and the irreversible entropy production in single
and multi-qubit examples.
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