Thermal contact: mischief and time scales

We discuss what kind of quantum dynamics can yield thermalization. We show that any temperature measurement protocol must be sensitive to the system's local energy scale, not just its state. Specifically, we illustrate this by showing that any temperature measurement protocol that does not resolve the system's local Hamiltonian (such as, e.g., full state tomography) is susceptible to being fooled into measuring any value for the temperature. Since placing a system in thermal contact with a reference system at a known temperature is a way of measuring temperature, any robust notion of thermal contact must be resistant to this ``attack''. This provides us with a necessary conditions for thermal contact between quantum systems. We then apply this condition to a scenario where one expects to find thermalization: a system repeatedly interacting with the microconstitutents of a thermal reservoir. We show such models of thermalization cannot be correct without fine-tuning.