Thermal states are the bedrock of statistical physics. Nevertheless, when and
how they actually arise in closed quantum systems is not fully understood. We
consider this question for systems with local Hamiltonians on finite quantum
lattices. In a first step, we show that states with exponentially decaying
correlations equilibrate after a quantum quench. Then we show that the
equilibrium state is locally equivalent to a thermal state, provided that the
free energy of the equilibrium state is sufficiently small and the thermal
state has exponentially decaying correlations. As an application, we look at a
related important question: When are thermal states stable against noise? In
other words, if we locally disturb a closed quantum system in a thermal state,
will it return to thermal equilibrium? We rigorously show that this occurs when
the correlations in the thermal state are exponentially decaying. All our
results come with finite-size bounds, which are crucial for the growing field
of quantum thermodynamics and other physical applications.Comment: 8 pages (5 for main text and 3 for appendices); v2 is essentially the
published versio
