Renormalized thermal entropy in field theory
Author(s): S. L. Cacciatori, F. M. Costa, F. Piazza
Journal: Phys. Rev. D
DOI Number: 10.1103/PhysRevD.79.025006
Link: Link to publication
Standard entropy calculations in quantum field theory, when applied to a subsystem of definite volume, exhibit area-dependent UV divergences that make a thermodynamic interpretation troublesome. In this paper we define a renormalized entropy which is related with the Newton-Wigner position operator.
Accordingly, whenever we trace over a region of space, we trace away degrees of freedom that are localized according to Newton-Wigner localization but not in the usual sense. We consider a free scalar field in d þ 1 spacetime dimensions prepared in a thermal state and we show that our entropy is free of divergences and has a perfectly sound thermodynamic behavior. In the high temperature/big volume limit our results agree with the standard QFT calculations once the divergent contributions are subtracted from the latter. In the limit of low temperature/small volume the entropy goes to zero but with a different
dependence on the temperature.Note: http://arxiv.org/abs/0803.4087 File: Link to PDF