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arXiv · 0803.4087

Renormalized Thermal Entropy in Field Theory

Sergio Cacciatori·Fabio Costa·Federico Piazza
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Abstract

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+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.

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Sergio Cacciatori, Fabio Costa, Federico Piazza. 2009-01-28. Renormalized Thermal Entropy in Field Theory. https://doi.org/10.1103/physrevd.79.025006

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