Thermodynamics, Statistical Mechanics and Large Deviations

Statistical mechanics of systems with long range interactions

Abstract. Many physical systems are governed by long range interactions, the main example being self-gravitating stars. Long range interaction implies a lack of additivity for the energy. As a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with many claims, the statistical mechanics of such systems is a well understood subject. In this proceeding, we explain...

Dephasing and dissipation in qubit thermodynamics.

We analyze the stochastic evolution and dephasing of a qubit within the quantum jump approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum thermodynamics and distributions in statistical mechanics. We demonstrate that dephasing and relaxation of the qubit render the Jarzynski and Crooks fluctu...

Large Deviations in Quantum Lattice Systems: One-Phase Region

The theory of large deviations studies the probability of rare events: It seeks to determine at which rate the probabilities of untypical events (large deviations) vanish, when measured with a family of distributions converging to a limit. This is a standard setup in equilibrium statistical mechanics. Imagine a very large (formally infinite) mechanical system which is in an equilibrium state co...

6 The theory of large deviations and applications to statistical mechanics

Studies in History and Philosophy of Modern Physics

In recent years a growing number of philosophers of science have come to realise that the philosophical foundations of statistical mechanics are not as secure as was once thought. Conceptual problems that had been swept under a carpet of technicalities, or simply ignored, have surfaced, solutions that were accepted are being questioned, and new routes are being explored. Thus, central issues su...