What is temperature, really?
Temperature is how fast a region's own clock runs against a local clock. Every state determines a flow, a clock made from nothing but the odds it holds, and the recipe is to take minus the logarithm of the state. Run it on a system with two possible answers, where the lower one turns up twenty times for every once the upper one does. The recipe returns log 20, about 2.996, and that number is the energy gap divided by the temperature. A thermometer supplies the scale. Halve the temperature with the energies fixed and twenty to one becomes four hundred to one, so the number doubles. Empty space has a temperature too, for anyone accelerating through it, at about four parts in 10²¹ of a degree for every meter per second squared.
Also in Chapter 22: Why Do All the Clocks Agree?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 21: Why Does Time Feel Like It's Moving?watch a universe make its own particles