- 96-429 Jaksic V., Pillet C.-A.
- Spectral Theory of Thermal Relaxation
Sep 20, 96
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Abstract. We review some results obtained in a recent series of papers on thermal
relaxation in classical and quantum dissipative systems. We consider models
where a small system S, with a finite number of degrees of freedom, interacts
with a large environment R in thermal equilibrium at positive temperature T.
The zeroth law of thermodynamics postulates that, independently of its initial
configuration, the system S evolves towards a unique stationary state. By
definition, this limiting state is the equilibrium state of S at temperature
T. Statistical mechanics further identifies this state with the Gibbs canonical
ensemble associated with S. For simple models we prove that the above picture
is correct, provided the equilibrium state of the environment R is itself
given by its canonical ensemble. In the quantum case we also obtain an exact
formula for the thermal relaxation time.