Landauer’s Princple for Fermionic Fields in One-Dimensional Bags

Abstract

In recent years, growing interest has been paid to the exploration of the concepts of entropy, heat and information, which are closely related to the symmetry properties of the physical systems in quantum theory. In this paper, we follow this line of research on the the validity of the concepts in quantum field theory by studying Landauer’s principle for a Dirac field interacting perturbatively with an Unruh–DeWitt detector in a 1+1-dimensional MIT bag cavity. When the field is initially prepared in the vacuum state, we find that the field always absorbs heat, while the Unruh–DeWitt detector can either gain or lose entropy, depending on its motion status, as a result of the Unruh effect. When the field is initially prepared in the thermal state and the detector remains still, the heat transfer and entropy change can be obtained under two additional but reasonable approximations: (i) one is where the duration of the interaction is turned on for a sufficiently long period, and (ii) the other is where the Unruh–DeWitt detector is in resonance with one of the field modes. Landauer’s principle is verified for both considered cases. Compared to the results of a real scalar field, we find that the formulas of the vacuum initial state differ solely in the internal degree of freedom of the Dirac field, and the distinguishability of the fermion and anti-fermion comes into play when the initial state of the Dirac field is thermal. We also point out that the results for a massless fermionic field can be obtained by taking the particle mass m→0 straightforwardly.