On a new definition of quantum entropy

Abstract

It is proved here that, as a consequence of the unitary quantum evolution, the expectation value of a properly defined quantum entropy operator (as opposed to the non-evolving von Neumann entropy) can only increase during non adiabatic transformations and remains constant during adiabatic ones. Thus Clausius formulation of the second law is established as a theorem in quantum mechanics, in a way that is equivalent to the previously established formulation in terms of minimal work principle [A. E. Allahverdyan and T. M. Nieuwenhuizen, Phys. Rev. E 71, 046107 (2005)]. The corresponding Quantum Mechanical Principle of Entropy Increase is then illustrated with an exactly solvable example, namely the driven harmonic oscillator. Attention is paid to both microcanonical and canonical initial condition. The results are compared to their classical counterparts.

4 pages, 3 figures

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Cited by in corpus (15)

• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• The quantum-classical correspondence principle for work distributions
• Employing Circuit QED to Measure Nonequilibrium Work Fluctuations
• Derivation of Boltzmann Principle
• Finite Bath Fluctuation Theorem
• Quantum Bochkov-Kuzovlev Work Fluctuation Theorems
• Fluctuation, Dissipation and the Arrow of Time
• Quantum to classical transition in the work distribution for chaotic systems
• Optimal protocols for Hamiltonian and Schrödinger dynamics
• Quantum Hertz entropy increase in a quenched spin chain
• Stiffness of Probability Distributions of Work and Jarzynski Relation for Non-Gibbsian Initial States
• Computing characteristic functions of quantum work in phase space
• Complementary expressions for the entropy-from-work theorem
• Increase of quantum volume entropy in presence of degenerate eigenenergies
• Evidence for simple "arrow of time functions" in closed chaotic quantum systems