  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 $O(\sqrt{mkT})$, 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
$O(\sqrt{mkT})$ 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.
