Thermodynamic Properties of Non-equilibrium States in Quantum Field Theory

Abstract

Within the framework of relativistic quantum field theory, a novel method is established which allows to distinguish non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with global equilibrium states (KMS states) by means of local thermal observables. With the help of such observables, the states can be ordered into classes of increasing local thermal stability. Moreover, it is possible to identify states exhibiting certain specific thermal properties of interest, such as a definite local temperature or entropy density. The method is illustrated in a simple model describing the spatio-temporal evolution of a "big heat bang".

Local Thermal Equilibrium States and Quantum Energy Inequalities

“…Let us now turn to the concept of local thermal equilibrium states introduced in [9] and further investigated in [8,10]. This will be done first for the case that the underlying spacetime is just Minkowski spacetime.…”

“…This will be done first for the case that the underlying spacetime is just Minkowski spacetime. Our discussion here is limited to the linear scalar field, but as explained in [9], the discussion can be generalized to include general quantum field theories. For the quantized linear scalar field on Minkowski spacetime, there is in each Lorentz frame a unique quasifree thermal equilibrium state at given temperature.…”

“…In the investigations of local thermal equilibrium for linear scalar fields φ(x) on Minkowski spacetime carried out in previous articles [8][9][10], the spaces S x are chosen as the linear spaces generated by elements s(x) = ð μ : φ 2 : (x), referred to as the balanced derivatives of the Wick-squared field : φ 2 : (x). 3 Here, μ = (μ 1 , .…”

“…Nevertheless, following a proposal by Buchholz, Ojima and Roos [9] and further investigated in [8,10], it is possible to introduce a covariant concept of states which, at given points x in spacetime, look like thermal equilibrium states with respect to a certain set, S x , of reference-observables. Such states are called local thermal equilibrium (LTE) states with respect to S x .…”

Action Ward Identity and the Stückelberg-Petermann Renormalization Group

“…In the off-shell formalism adopted here, however, one can actually show that there are no anomalies for the AWI. Namely one may introduce balanced fields, as was done recently for the purpose of non-equilibrium quantum field theory by Buchholz, Ojima and Roos [6]: the balanced fields form that subspace P bal of all local fields…”