Any theory or explanation on the relation between temperature and causality? Any theory or explanation on the relation between temperature and causality?
I guess causality is correlated to information and temperature.
 A: There is and is not, depending if you are concerned with equilibrated systems (in thermal equilibrium) or slightly perturbed systems. Let's look at temperature, T, for a system that in thermal equilibrium.
$T := \frac{\partial U}{\partial S}$ where all other state variables are held fixed where $S$ the entropy and $U$ is the internal energy. One can see that if one adds $x$ units of entropy, the amount of $x T$ in internal energy change can be seen. Further note that for systems in thermal equilibrium, the temperature is constant over time and space.
If you want to link Temperature (in this case) with causality you would have to argue if temperature of the system affects the order of events.
In hydrodynamics, one often considers small gradients of Temperature over space and time. Then you could wonder if a small perturbation of Temperature, how fast would that disturbance reach another point (some time later and at a different location). Understanding this speed needs more knowledge of the microscopic theory which would also have to be known to derive the internal energy state equation. For example, think speed of sound in air, which depends on Temperature.
