Finite energy but infinite entropy production from moving mirrors

Abstract

Accelerating mirrors provide a simple conceptual laboratory for studying particle production and the relation between trajectory and particle, energy, and entropy fluxes. We focus on the relation between energy and entropy, studying some special cases with finite total energy but infinite integrated entropy (though the entropy flux may be finite at any particular moment). We present a new asymptotically static moving mirror trajectory with solvable beta Bogolyubov coefficients, total energy, and fully relativistic particle count. The integrated entropy diverges despite finite global radiative particle and energy emission. By comparing closely related trajectories, we point out some general principles (e.g., the asymptotic time dependence of energy flux and entropy flux for different convergence and divergence behaviors) but also how subtle distinctions can affect the physics and its relation to black hole end states. Another class of models includes exponentially accelerated mirrors in proper time; one of its unexpected behaviors is finite energy emission but divergent entropy. We compare mirrors exponentially accelerated in other coordinates as well, showing their close relation and an interesting duality property.