For almost all pure states sampled from the Scrooge measure, entropy production is exponentially close to the ensemble value, so typical pure states obey the second law.
The second law of Thermodynamics as a theorem in quantum mechanics
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We treat a quantum mechanical system with certain general properties which are expected to be common in macroscopic quantum systems. Starting from a PURE initial state (which may not describe an equilibrium) in which energy is mildly concentrated at a single value, we consider a time evolution determined by a time-dependent Hamiltonian as a model of an adiabatic operation in thermodynamics. We take a family of operations with the same procedure and various ``waiting times.'' Then the Minimum Work Principle is rigorously proved for almost all choices of the waiting time.
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cond-mat.stat-mech 1years
2024 1verdicts
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Typical Positivity of Nonequilibrium Entropy Production for Pure States
For almost all pure states sampled from the Scrooge measure, entropy production is exponentially close to the ensemble value, so typical pure states obey the second law.