Thermodynamic entropy production in the dynamical Casimir effect

We address the question of entropy production in the context of the dynamical Casimir effect. Specifically, we consider a one-dimensional ideal cavity with one of its mirrors describing a prescribed trajectory. Inside the cavity we have a scalar quantum field and we ask about the changes in the thermodynamic entropy of the field induced by the non-trivial boundary conditions imposed by the moving mirror. By employing an effective Hamiltonian approach, we compute the entropy production and show that it scales with the number of particles created in the short-time limit. Moreover, such approach allows us to demonstrate that this entropy is directly related to the developments of quantum coherences in the mode basis of the field. A distinct approach, based on the time evolution of Gaussian states, allows us to study the long-time limit of the entropy production in single mode of the field. This results in a relation between the thermodynamic entropy production in the field mode with the entanglement between the considered mode and all the other modes. In this way, we link the entropy production in the field due to the dynamical Casimir effect with two fundamental features of quantum mechanics, coherence and entanglement.Comment: 11 pages, 1 figure, comments are welcom