Basic Problems in Statistical Mechanics


Our first main objective is to understand and extend the concept of "system and environment" on a microscopic basis, in particular in non-equilibrium setups and/or when one has to go beyond the usually considered weak coupling assumption between system and bath. A further issue is the generalization of concepts from equilibrium thermodynamics and statistical mechanics for systems far from thermal equilibrium by means of methods from nonlinear dynamics. Closely related to both issues are the problems of the microscopic foundation of basic statistical mechanical principles and of irreversibility. The two main results in this context are:

(i) For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given realistic observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and nonequilibrium conditions. In other words, there is a huge set of pure states (zero entropy) each of which imitates a given statistical ensemble to the extent that experimentally it is practically impossible to see a difference.

(ii) We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared to the resolution limit. Both properties are fulfilled under many, if not all, experimentally realistic conditions. At equilibrium, the predictions and limitations of Statistical Mechanics are recovered. In other words, equilibrium Statistical Mechanics is derived from standard Quantum Mechanics without any additional ``principle'' or ``postulate'' apart from the above mentioned assumptions about realistic observables and initial conditions (work in progress).

Selected publications:

P. Reimann
A Uniqueness-Theorem for "Linear" Thermal Baths
Chem. Phys. 268, 337 (2001)

P. Reimann
Brownian Motors: Noisy Transport far from Equilibrium
Phys. Rep. 361, 57 (2002)

P. Reimann
Typicality for Generalized Microcanonical Ensembles
Phys. Rev. Lett. 99, 160404 (2007)

P. Reimann
Typicality of Pure States Randomly Sampled According to the Gaussian Adjusted Projected Measure
J. Stat. Phys. 132, 921 (2008)

P. Reimann
Foundation of Statistical Mechanics under Experimentally Realistic Conditions
Phys. Rev. Lett. 101, 190403 (2008)

P. Reimann
Canonical thermalization
New J. Phys. 12, 055027 (2010)

P. Reimann and M. Kastner
Equilibration of isolated macroscopic quantum systems
New J. Phys., in press

Last modified on 2012-03-14