The dynamical Casimir effect and the generation of thermodynamic entropy

Abstract

In this dissertation, we investigate the dynamics of the thermodynamic entropy production in the dynamical Casimir effect. This is done by considering a quantum scalar field confined by a one-dimensional cavity composed of a pair of ideal mirrors, one fixed and the other allowed to move in a prescribed trajectory. The central goal of this work is to understand how the thermodynamic entropy of the field evolves over time due to the particle creation process induced by the non trivial boundary conditions imposed by the moving mirror. By employing an effective Hamiltonian approach, the system’s entropy production is shown to increase with the number of particles created within the short-time limit. Moreover, one can also demonstrate that this approach is directly related to the generation of quantum coherence in the energy basis of the field. Utilizing a distinct method, grounded in the theory of Gaussian states, we were able to analyze the long-time limit of the entropy production for a single mode of the field. The obtained results establish a relationship between the increase in thermodynamic entropy in the field mode and the entanglement between the considered mode and the rest of the field mode structure. In this way, we link the entropy production in the field due to the dynamical Casimir effect with two fundamental features of quantum mechanics: quantum coherence and entanglement.