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Quantum heat-up operation and violation of the second law of thermodynamics

Toward the formulation of the operational approach to quantum thermodynamics, the heat-up operator is explicitly constructed. This quantum operation generates for a generic system an irreversible transformation from a pure ground state at zero temperature to a state at finite temperature. The fixed point analysis shows that repeated applications of the operation map from an arbitrary state to the completely random state realized in the high-temperature limit. The change of the von Neumann entropy is evaluated for a simple bipartite spin-1/2 system. It is shown that remarkably, the second law of thermodynamics may be violated along processes generated by the present quantum operation.