# The Definition of Temperature in a Statistical Manner

I am new in thermal physics and I started studying recently the canonical ensemble.

Until now, I understand that, in thermal equilibrium, the temperature and energy content of two systems placed in thermal contact with each other but thermally isolated from the surroundings will no longer be changing with time (in the thermodynamic limit, because there will still be somo fluctuations, but they are negligible).

We also define temperature in a statistical manner, and we relate it to the number of microstates the system can be with the energy available, more precisely:

$$\frac{1}{k_bT} = \frac{\text d(ln(\Omega))}{\text dE}$$

So we relate the temperature with a microscopic property... And my question is:

We relate the temperature with a “microscopic configuration of the system”, does that mean the temperature is a microscopic property of the system?

• What do you mean by a "microscopic property"? Commented Dec 10, 2019 at 22:43
• In the same way that we can define the system by the microstate and / or the macrostate
– user249212
Commented Dec 10, 2019 at 22:45
• I suppose that a system have some macroscopics properties such as the pressure or the volume that we can actually measure, and then we have the microscopic properties such as the description of the motion of each individual molecule
– user249212
Commented Dec 10, 2019 at 22:47
• No, temp. is a macrostate. Commented Dec 11, 2019 at 7:01