Statistical mechanics of generally covariant quantum theories: A Boltzmann-like approach

Details Statistical mechanics of generally covariant quantum theories: A Boltzmann-like approach Statistical mechanics of generally covariant quantum theories: A Boltzmann-like approach

2000-02-04

arxiv.org/abs/gr-qc/0002024v2

Class.Quant.Grav. 18 (2001) 555-569

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, no figures, Latex file. Revised version. Accepted for publication in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/18/3/314

We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of energy and external time. We consider a composite system formed by a large number of identical components, and apply Boltzmann's ideas and the fundamental postulates of ordinary statistical physics. The thermodynamical parameters are determined by the properties of the thermalizing interaction. We apply these ideas to a simple example, in which the component system has one physical degree of freedom and mimics the constraint algebra of general relativity.

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