The Vlasov-Maxwell statistical treatment of relativistic charged particles subject to electromagnetic (EM) radiation reaction (RR) represents an unsolved conceptual challenge. In fact, as shown here, the customary point-particle treatment based on the Landau-Lifschitz (LL) equation leads to a generally nonconstant Boltzmann-Shannon (BS) entropy even in the absence of binary collisions. This conclusion appears to be in contradiction with the intrinsic microscopic reversibility of the underlying physical system. In this paper the issue is addressed in the framework of a Hamiltonian treatment for extended charged particles in the presence of EM RR. It is shown that such a behavior actually has no physical ground, being a consequence of the asymptotic approximations involved in the construction of the LL equation. In particular, it is proved that the Hamiltonian structure of the underlying particle dynamics actually restores the conservation of the BS entropy. The connection between the two approaches is analyzed. As a result, it is pointed out that the fulfillment of the entropy law can still be warranted even in the framework of an asymptotic theory by introducing a suitable Hamiltonian approximation for the EM RR equation.

• Received 16 January 2013

DOI:https://doi.org/10.1103/PhysRevE.87.032107