Time and temperature in quantum physics

Abstract: For many people a clock is the epitome of a predictable, reversible dynamical system. Yet we are all familiar with the irreversible clocks used in radio carbon dating.  Much earlier, Mach and Eddington both proposed irreversible thermal clocks.  In general relativity the Tolman relations connect the local measurements of time and temperature.   Rovelli’s thermal time hypothesis uses thermal equilibrium states to define the local flow of time in general relativity. Given a good clock it is possible to make local measurements of temperature and, conversely, given a good thermometer it is possible to make a local clock. There is thus a kind of duality to time and temperature.  I will illustrate this concept using a physical example based on quantum opto-mechanics.