%0 Journal Article %T On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas %A P¨¦ter B¨˘lint %A Thomas Gilbert %A P¨¦ter N¨˘ndori %A Domokos Sz¨˘sz %A Imre P¨¦ter T¨®th %J Mathematics %D 2015 %I arXiv %X 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. %U http://arxiv.org/abs/1510.06408v1