  Thermalization is the ubiquitous phenomenon of a system attaining thermal
equilibrium. When a small system (probe) is connected to a larger one,
thermalization entails induction of the temperature of the larger system onto
the smaller one. We introduce the notion of phase thermalization, a phenomenon
where the quantum phase of a large system is induced onto a smaller one. We
provide an explicit example where the smaller system is a heavy Fermi liquid
and the larger system is an incoherent metal.
