caa a22 4500 467891826 CHVBK 20180406152751.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s10955-006-9129-4 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9129-4 Tasaki Hal Department of Physics, Gakushuin University, Mejiro, Toshima-ku, 171-8588, Tokyo, Japan aut The Coefficient of Restitution Does Not Exceed Unity [Elektronische Daten] [Hal Tasaki] We study a classical mechanical problem in which a macroscopic ball is reflected by a non-deformable wall. The ball is modeled as a collection of classical particles bound together by an arbitrary potential, and its internal degrees of freedom are initially set to be in thermal equilibrium. The wall is represented by an arbitrary potential which is translation invariant in two directions. We then prove that the final normal momentum can exceed the initial normal momentum at most by O(■mkT), where m is the total mass of the ball, k the Boltzmann constant, and T the temperature. This implies the well-known statement in the title in the macroscopic limit where O(■mkT) is negligible. Our result may be interpreted as a rigorous demonstration of the second law of thermodynamics in a system where a macroscopic dynamics and microscopic degrees of freedom are intrinsically coupled with each other. Springer Science + Business Media, Inc., 2006 second law of thermodynamics nationallicence coefficient of restitution nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/6(2006-06-01), 1361-1374 0022-4715 123:6<1361 2006 123 10955 https://doi.org/10.1007/s10955-006-9129-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9129-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tasaki Hal Department of Physics, Gakushuin University, Mejiro, Toshima-ku, 171-8588, Tokyo, Japan aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/6(2006-06-01), 1361-1374 0022-4715 123:6<1361 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer