INCREASE-IN-ENTROPY LAW

An increase-in-entropy law is derived from two very simple and direct premises: First, the probability distribution function describing the states of the system depends only on the macroscopic information that an observer can obtain by a measurement of the constraints imposed on the system. Second, each time a measurement is performed the observation generates information that depends only on the present state of the system, a fact which is explicitly determined by the mathematical properties of Ehrenfest's coarse-graining procedure, shown here to be identical to the action of Zwanzig's projection operator on the true N-body distribution function. Further, the act of observation is restricted to take place in time intervals that cannot be smaller than a collision time nor larger than the relaxation time to assure the full meaning of a statistical average. Under these conditions the process governing the time-dependent statistical phenomena is shown to be Markovian, although not necessarily linear in the variables associated with the observables of the system. The results are also placed within the context of previous work done along these lines.