Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
arXiv:1507.06479 · doi:10.1007/s10955-016-1511-2
Abstract
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems. We first formulate the notion that a pure state in an isolated quantum system represents thermal equilibrium. Then by assuming, or proving in certain classes of nontrivial models (including that of two bodies in thermal contact), large-deviation type bounds (which we call thermodynamic bounds) for the microcanonical ensemble, we prove that to represent thermal equilibrium is a typical property for pure states in the microcanonical energy shell. We believe that the typicality, along with the empirical success of statistical mechanics, provides a sound justification of equilibrium statistical mechanics. We also establish the approach to thermal equilibrium under two different assumptions; one is that the initial state has a moderate energy distribution, and the other is the energy eigenstate thermalization hypothesis.
73 pages, 5 figures. Minor improvements have been made in ver 4. References [49] and [62] have been added. The paper will be published in Journal of Statistical Physics
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