statistical mechanics -- why is temperature not a mechanical variable Hi, I have heard that temperature is not a mechanical variable. That is, that even if you knew the positions and momenta of all the particles in some system, you still couldn't calculate the temperature, because temperature (and entropy, and free energy, etc) are ensemble variables. Why is that? By the way, one implication of this statement is that temperature is not really the average kinetic energy of a system, at least in some cases. Say you had a dilute (better yet, ideal) system of independent gas (argon) atoms and you knew the mass of any particle (they all have the same mass) and its velocity. You could then calculate kinetic energy (0.5 * m*v*v, right?) and average kinetic energy, therefore kinetic energy (and average kinetic energy) is a mechanical variable. But temperature is not. So temperature is not really average kinetic energy. So, what is temperature? Thanks!