Emergence of equilibrium thermodynamic properties in quantum pure states. I. Theory

Journal Article · Wed Jul 21 00:00:00 EDT 2010 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3455998· OSTI ID:21559886

Fresch, Barbara; Moro, Giorgio J ^[1]

---

1. Department of Chemical Science, University of Padova, Via Marzolo 1, Padova 35131 (Italy)

Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum systems. In the present contribution a simple but effective theoretical framework is introduced to clarify the connections between a purely mechanical description and the thermodynamic characterization of the equilibrium state of an isolated quantum system. A salient feature of our approach is the very transparent distinction between the statistical aspects and the dynamical aspects in the description of isolated quantum systems. Like in the classical statistical mechanics, the equilibrium distribution of any property is identified on the basis of the time evolution of the considered system. As a consequence equilibrium properties of quantum system appear to depend on the details of the initial state due to the abundance of constants of the motion in the Schroedinger dynamics. On the other hand the study of the probability distributions of some functions, such as the entropy or the equilibrium state of a subsystem, in statistical ensembles of pure states reveals the crucial role of typicality as the bridge between macroscopic thermodynamics and microscopic quantum dynamics. We shall consider two particular ensembles: the random pure state ensemble and the fixed expectation energy ensemble. The relation between the introduced ensembles, the properties of a given isolated system, and the standard quantum statistical description are discussed throughout the presentation. Finally we point out the conditions which should be satisfied by an ensemble in order to get meaningful thermodynamical characterization of an isolated quantum system.

• OSTI ID: 21559886
• Journal Information: Journal of Chemical Physics, Vol. 133, Issue 3; Other Information: DOI: 10.1063/1.3455998; (c) 2010 American Institute of Physics; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
ABUNDANCE
AUGMENTATION
DISTRIBUTION
ENTROPY
EQUILIBRIUM
FUNCTIONS
NONLINEAR PROBLEMS
PROBABILITY
PURE STATES
QUANTUM INFORMATION
QUANTUM MECHANICS
SCHROEDINGER EQUATION
STATISTICAL MECHANICS
THERMODYNAMICS
DIFFERENTIAL EQUATIONS
EQUATIONS
INFORMATION
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
QUANTUM STATES
THERMODYNAMIC PROPERTIES
WAVE EQUATIONS