On the Semiclassical Transition in the Quantum Gibbs Distribution

An example of a Gibbs ensemble for a system of $N$ Brownian particles is given, and the relation with Kolmogorov complexity is considered. The irreversibility of the process is analyzed and shown to be a consequence of the loss of numbering of the particles. The dependence of the measure in the semiclassical Gibbs distribution on temperature is studied in examples.