Statistical Ensemble and Quantization of Thermodynamics

Jean Brunet

Jurij Avsec, Milan Marčič

Л. В. Кулик, L. I. Musina, E. I. Belozerov +2 more

Abstract Two-dimensional electronic systems in a quantizing magnetic field are of great interest when using quasiparticles with non-Bose and non-Fermi (anyon) statistics in solving problems of applied physics. The fractional quantum Hall effect states have so far been the only candidates for the role of quasiparticle systems with anyon statistics. Nonequilibrium macroscopic ensembles of neutral excitations in the 1/3 fractional quantum Hall effect are created to determine the statistical and thermodynamic properties of anyon systems and the applicability of anyons in solving technological tasks. It is found these ensembles have such long periods of relaxation they may be considered new quasi-equilibrium states of anyon matter.

Paul Boes, Henrik Wilming, Jens Eisert +1 more

Maximum-entropy ensembles are key primitives in statistical mechanics. Several approaches have been developed in order to justify the use of these ensembles in statistical descriptions. However, there is still no full consensus on the precise reasoning justifying the use of such ensembles. In this work, we provide an approach to derive maximum-entropy ensembles, taking a strictly operational perspective. We investigate the set of possible transitions that a system can undergo together with an environment, when one only has partial information about the system and its environment. The set of these transitions encodes thermodynamic laws and limitations on thermodynamic tasks as particular cases. Our main result is that the possible transitions are exactly those that are possible if both system and environment are assigned the maximum-entropy state compatible with the partial information. This justifies the overwhelming success of such ensembles and provides a derivation independent of typicality or information-theoretic measures.

Peter Hertel

Laszlo Tisza