Emergence of equilibrium thermodynamic properties in quantum pure states. II. Analysis of a spin model system

The Journal of Chemical Physics
Barbara Fresch, Giorgio J Moro

Abstract

A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and of the equilibrium reduced density matrix of a subsystem for the two different statistics introduced in Part I. In order to analyze their consistency with thermodynamics, these quantities of interest are evaluated in the limit of large number of components of the isolated system. The main results can be summarized as follows: typical values of the entropy and of the equilibrium reduced density matrix as functions of the internal energy in the fixed expectation energy ensemble do not satisfy the requirement of thermodynamics. On the contrary, the thermodynamical description is recovered from the random pure state ensemble (RPSE), provided that one considers systems large enough. The thermodynamic limit of the considered properties for the spin system reveals a number of important features. First canonical statistics (and thus, canonical typicality as long as the fluctuations around the average value are small) emerges without the need of assuming the microcanonical space for the global pure st...Continue Reading

References

Feb 21, 2006·Physical Review Letters·Sheldon GoldsteinNino Zanghì
Apr 7, 2006·Nature·Kwing-So Choi
Feb 13, 2008·The Journal of Chemical Physics·Dieter Suter, T S Mahesh
Dec 24, 2009·The Journal of Physical Chemistry. a·Barbara Fresch, Giorgio J Moro
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Boris V Fine

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Citations

Feb 10, 2011·The Journal of Chemical Physics·Barbara Fresch, Giorgio J Moro
May 11, 2016·The Journal of Physical Chemistry. a·Maurizio CodenGiorgio J Moro
Jun 27, 2017·The Journal of Physical Chemistry. a·Francesco Avanzini, Giorgio J Moro
Nov 29, 2017·Physical Chemistry Chemical Physics : PCCP·Francesco Avanzini, Giorgio J Moro
Jan 14, 2017·Physical Review. E·Walter Hahn, Boris V Fine
Aug 27, 2011·Physical Review Letters·Kai Ji, Boris V Fine
Aug 30, 2017·The Journal of Physical Chemistry. a·Maurizio CodenBarbara Fresch

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Software Mentioned

RPSE
FEEE

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