Quantum thermodynamics of ergotopy for a relativistic battery as a witness to Unruh–Hawking thermality in curved (A)dS spacetimes

Abstract

We propose a relativistic quantum battery model consisting of an accelerated Unruh–DeWitt detector coupled to a massless scalar field in a de Sitter and anti-de Sitter spacetimes. The maximal amount of quantum extractable work, defined as the ergotropy, is used to probe Unruh–Hawking thermality induced by acceleration and spacetime curvature. Using the open quantum system approach, we study the dynamics of the ergotropy with respect to the Kubo–Martin–Schwinger temperature, spacetime boundary conditions, and dimensionality. It has been found that the asymptotic value of quantum work extraction is determined solely by the acceleration and curvature. The steady behavior in the two spacetimes can be unified to witness the Unruh–Hawking thermality which is independent of boundary conditions and dimensionality. From a perspective of time-dependent evolution, we investigate how the ergotropy evolves through different pathways as the battery gradually reaches the same thermal equilibrium state characterized by a certain KMS temperature. In dS spacetime, the evolution at large acceleration exhibits pronounced oscillations and differs from the fast thermal relaxation observed at low acceleration. Varying the boundary condition in AdS can improve the energy storage of the moving battery. When the dimension of AdS is increased, vacuum fluctuations can modestly amplify the ergotropy in the initial stage and facilitate the rapid thermalization. From the perspective of energy transfer, the relativistic quantum battery helps explore the thermal vacuum in curved spacetimes.