# Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization

February 22, 2024

For any local, translation-covariant quantum field theory on Minkowski
spacetime we prove that two distinct primary states that are invariant under
the inertial time evolutions in different inertial reference frames and satisfy
a timelike cluster property called the mixing property are disjoint, i.e. each
state is not a perturbation of the other. These conditions are fulfilled by the
inertial KMS states of the free scalar field, thus showing that a state
satisfying the KMS condition relative to one reference frame is far from
thermal equilibrium relative to other frames. We review the property of return
to equilibrium in open quantum systems theory and discuss the implications of
disjointness on the asymptotic behavior of detector systems coupled to states
of a free massless scalar field. We argue that a coupled system consisting of
an Unruh-DeWitt detector moving with constant velocity relative to the field in
a thermal state, or an excitation thereof, cannot approach a KMS state at late
times under generic conditions. This leads to an illustration of the physical
differences between heat baths in inertial systems and the apparent "heat bath"
of the Unruh effect from the viewpoint of moving detectors. The article also
reviews, from a quantum field theoretical perspective, the quantum dynamical
system of an Unruh-DeWitt detector coupled to a massless scalar field in a KMS
state relative to the rest frame of the detector.

Keywords:

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