Finite Energy but Infinite Entropy Production from Moving Mirrors

TL;DR

This paper investigates moving mirror models that produce finite energy but infinite entropy, revealing novel behaviors and dualities in particle and entropy fluxes with exact solutions.

Contribution

It introduces new mirror trajectories with solvable parameters showing finite energy emission but divergent entropy, expanding understanding of particle production.

Findings

Finite total energy with infinite integrated entropy in certain mirror models.

Explicit solutions for asymptotically static and exponentially accelerated mirrors.

Discovery of duality relations between different mirror acceleration scenarios.

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. 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.