In this mindset, there makes no sense of defining temperature of very far out of equilibrium (i.e., very non-boltzmann like) systems, because it's possible to get all kinds of non-sense and almost sensible but confusing answers.Īs far as I found, they use this RMS average to find each kind of temperature, kinectic, rotational or vibrational. So, the use the equipartition theorem, which relates the RMS average of quadratic quantities of the energy to the temperature, is conditioned to the system being on local thermodynamical equilibrium. Note that one can relate the RMS average of this distribution to the width (consequently to the temperature), but it's not always true the other way around. The temperature of the system is identified, if the system have a boltzmann like momentum distribution, to the momentum width of this distribution. The idea behind the connection of thermodynamics and Boltzmann equation is to extend this solution that is independent of both position and time, i.e., it's a global equilibrium solution, to a local solution, thus, having a position and time dependent temperature. The Sutherland formula is a phenomenological formula, but if you do molecular dynamics, or use a Boltzmann solver, then you can compute the viscosity microscopically, using the Kubo relation 1) I am not exactly sure what you have in mind.
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