PreprintCC BY 4.0arXiv
First integrals of dense hard-ball gases
Abstract
We answer two questions of Kozlov about polynomial-in-momentum first integrals of billiard systems. For billiards in bounded polytopes, such integrals are independent of position. For hard-ball gases in a rectangular box, every polynomial-in-momentum first integral is a polynomial in the total kinetic energy whenever the collision graph is connected.
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BibTeX
@misc{smirnov2026first,
title = {{First integrals of dense hard-ball gases}},
author = {Gleb Smirnov},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29694},
eprint = {2608.29694},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29694},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - First integrals of dense hard-ball gases
AU - Gleb Smirnov
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29694
UR - https://arxiv.org/abs/2608.29694
AB - We answer two questions of Kozlov about polynomial-in-momentum first integrals of billiard systems. For billiards in bounded polytopes, such integrals are independent of position. For hard-ball gases in a rectangular box, every polynomial-in-momentum first integral is a polynomial in the total kinetic energy whenever the collision graph is connected.
ER -