Local Thermal Equilibrium States and Quantum Energy Inequalities

Abstract

Abstract. In this paper we investigate the energy distribution of states of a linear scalar quantum field with arbitrary curvature coupling on a curved spacetime which fulfill some local thermality condition. We find that this condition implies a quantum energy inequality for these states, where the (lower) energy bounds depend only on the local temperature distribution and are local and covariant (the dependence of the bounds other than on temperature is on parameters defining the quantum field model, and on local quantities constructed from the spacetime metric). Moreover, we also establish the averaged null energy condition (ANEC) for such locally thermal states, under growth conditions on their local temperature and under conditions on the free parameters entering the definition of the renormalized stress-energy tensor. These results hold for a range of curvature couplings including the cases of conformally coupled and minimally coupled scalar field.

Local thermal equilibrium and KMS states in curved spacetime

“…It was argued in [7,22,23] that, in curved spacetime, local concepts may replace the global ones involved in the definition of equilibrium. In locally covariant QFT [3], one can use point-like localized observables which are sensitive to thermal properties of global equilibrium states in Minkowski spacetime in order to attach local thermal parameters like a temperature to "local thermal equilibrium" (LTE) states in curved spacetime.…”

Local Thermal Equilibrium States in Relativistic Quantum Field Theory

“…Such a generalized KMS condition, called local KMS condition, has been introduced in [14], and it turns out that, under additional (physically motivated) analyticity assumptions on the two-point function, both approaches yield the same class of non-equilibrium states of the quantized Klein-Gordon field on Minkowski spacetime. Finally, we want to mention that the concept of LTE states has also been generalized to include quantum fields on a generic curved spacetime [11,22,24] and some results concerning the thermal behaviour of quantum fields in cosmological spacetimes of Friedmann-Robertson-Walker type [28] have been established [13,18,21]. For an overview and a more in-depth discussion of these results and other results concerning LTE states in quantum field theory, we refer the interested reader to the exhaustive review article by Verch [27] and the references therein.…”

Algebraic Quantum Field Theory in Curved Spacetimes

“…This is a class of states to which one can, approximately, ascribe a temperature at each point in spacetime, where the temperature together with the temperature rest frame is a function of the spacetime point. This class of states was introduced in [29] and further investigated in [27]; some applications to quantum fields in curved spacetime appear in [158,138,142,143].…”