ABSTRACT
Q: Wait! What is the system? What is the reservoir? If the box is insulated then isn’t this a microcanonical ensemble?
A: These are all excellent questions. The system is a single particle [atom or molecule] of gas and the reservoir consists of the remaining N particles. The single atom interacts [weakly] through collisions with the other atoms and is thus able to gain and lose [thermal] energy. [We implicitly assume that thermal energy can be gained in any amount-eschewing quantisationand that the distributions governing particle position and velocity are continuous.] As has been our practice, we assume that there are no long-range interactions among the gas atoms and that the effects of gravity are negligible. [Therefore the physical situation is both homogeneous and isotropic provided that N , V , and T are sufficiently large.]
The state of the system is fully described by the [3-d] position, ~r, and [3-d] velocity,1 ~v, of the single gas particle. The kinetic energy of the system is K = 12 mv
2. Potential energy terms, should they exist, are irrelevant to this system [by assumption].
