# Billiards, invariant measures, and equilibrium thermodynamics. II

Source: [Billiards, invariant measures, and equilibrium thermodynamics. II](<https://www.sota2.com/research/paper/68fa1f977a2b558e2932ac4f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T18:51:19.586Z

Authors: V.V. Kozlov

Published: 2005-03-09T13:56:21.000Z

## Abstract

The kinetics of collisionless continuous medium is studied in a bounded region on a curved manifold. We have assumed that in statistical equilibrium, the probability distribution density depends only on the total energy. It is shown that in this case, all the fundamental relations for a multi-dimensional ideal gas in thermal equilibrium hold true.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/nlin/0503018>)

[PDF](<https://arxiv.org/pdf/nlin/0503018.pdf>)