Statistical ensembles and X-probability

TL;DR

This paper challenges the traditional view of statistical ensembles, arguing they result from internal probabilistic processes rather than environmental influence, and clarifies the relationship between canonical and microcanonical distributions.

Contribution

It introduces a new perspective that internal probabilistic processes generate statistical ensembles, contrasting with the conventional environmental influence explanation, and clarifies the derivation of canonical distribution.

Findings

Contradictions in ensemble interpretation when considering environmental influence.

Canonical distribution results from averaging microcanonical ensemble, not independence.

Internal probabilistic processes are essential for understanding statistical ensembles.

Abstract

We show insurmountable contradictions which arise if statistical ensembles are considered a consequence of the influence of the environment of the physical systems. We regard the multiplicity of states with a definite energy value as a result of internal probabilistic processes in the macrosystem; these internal probabilistic processes are not taken into account by quantum mechanics. On a simple example it is demonstrated, that canonical distribution is not independent and equal to microcanonical one, but is a result of averaging by microcanonical ensemble.