# On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas

Source: [On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas](<https://www.sota2.com/research/paper/68fa340f1e209131ce895807>)

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

Data updated: 2025-10-24T20:26:12.151Z

Authors: P\\'eter B\\'alint, Thomas Gilbert, P\\'eter N\\'andori, Domokos Sz\\'asz, Imre P\\'eter T\\'oth

Published: 2015-10-21T20:09:38.000Z

## Abstract

We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a \`piston', i.e. a line-segment, which moves back and forth along a one-dimensional interval partially intersecting the cell. This model can be considered as the elementary building block of a spatially extended high-dimensional billiard modeling heat transport in a class of hybrid materials exhibiting the kinetics of gases and spatial structure of solids. Using heuristic arguments and numerical analysis, we argue that, in a regime of rare interactions, the billiard process converges to a Markov jump process for the energy exchanges and obtain the expression of its generator.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1510.06408>)

[PDF](<https://arxiv.org/pdf/1510.06408.pdf>)