Recently I have been very interested in the concept of a thermal time. The basic premise is that unidirectional time coordinate we experience may not be a fundamental property of some GUT (grand unified theory) scale physics but is instead an emergent phenomenon. At first this sounds somewhat anarchical as physical laws mostly focus on predicting the state of a system at some future time and almost invariably involve some kind of description of the behaviors of a system under dynamical evolution.  The idea is at once fascinating but also unconventional enough to be something you need a really good reason for doing. If you are genuinely curious try reading Rovelli and Connes [1].

The story begins with the Tolman Ehrenfest effect. Static observers who measure Temperature in gravitational fields find that it depends on the gravitational potential at the point where the measurement is made so that

is a constant (interestingly this scaling is usually associated with the relation between the coordinate time and the proper time measured by a clock traveling along a world line) [2,3].  In other words a long column of fluid in thermal equilibrium will naturally have a temperature gradient with hotter liquid at the bottom.  The difference is tiny; nevertheless it implies general relativity is deeply intertwined with the temperature of your beer tower.

What if at some level statistical physics and thermodynamics are fundamental and what we perceive as time is an emergent property. We can postulate that the universe is described by a generally covariant theory which treats all coordinate directions  evenhandedly and time is an artifact of the thermal state that we are immersed in.

There is no place for a preferred time variable in general relativity; furthermore if we look at the physically observable quantity measured by a clock it is in fact the proper time along a world line.  The coordinate time which parameterizes the field variables,