Stiffness of Probability Distributions of Work and Jarzynski Relation for Non-Gibbsian Initial States

Abstract

We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. Our point of departure is the assumption that, if systems start in microcanonical states at some initial energies, the resulting probability distributions of work may be largely independent of the specific initial energies. It is demonstrated that this assumption has some far-reaching consequences, e.g., it implies the validity of the Jarzynski relation for a large class of non-Gibbsian initial states. By performing numerical analysis on integrable and non-integrable spin systems, we find the above assumption fulfilled for all considered examples. Through an analysis based on Fermi's Golden Rule, we partially relate these findings to the applicability of the eigenstate thermalization ansatz to the respective driving operators.

16 pages, 14 figures

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• A framework for sequential measurements and general Jarzynski equations
• Stiffness of Probability Distributions of Work and Jarzynski Relation for Initial Microcanonical and Energy Eigenstates
• The second law of thermodynamics from concavity of energy eigenvalues
• Modified Jarzynski equality in a microcanonical ensemble
• Integral Fluctuation Theorem for Microcanonical and Pure States
• The second law of thermodynamics from concave energy in classical mechanics
• False Onsager relations