Boltzmann was the first person to set up a viable theory of non-equilibrium thermodynamics. To do this, he had to give a much more detailed description of "state". Until then, a state was described by a few parameters, such as V,P or P,T and so on. The non-equilibrium state was then taken to be described by say V(t),P(t), where t is the time. One might then change the coordinates to P(t), T(t). But this is useless, since the relation between V, T and P given by the equation of state holds only at equilibrium, and we do not know what relation we are to use if we are not in equilibrium. So the manifold of states (in Carathéodory's formulation) has not got two dimensions at each time. In Boltzmann's theory, the state is given by a very large number of variables, and the equation of motion was also given. The macroscopic variables were given by averages of these microvariables. I modelled my book statistical dynamics on this idea, incorporating our present knowledge about the quantum nature of the energy levels, identical particles etc. This leads to a more realistic theory than that based on classical spherical particles, as in Boltzmann's original attempt.
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© by Ray Streater, 13/6/00.