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Phase Space Evolution in Phase Space A general definition of entropy was formulated by Boltzmann in 1872. It is expressed in terms of "coarse-graining volume" in the phase space, which amalgamates the positions and momenta of all particles in a system into one point (Figure 01f). The relentless increase toward higher entropy until reaching its maximum (i.e., in a state of thermal equilibrium) is related to the fact that the

Figure 01f Phase Space [view large image]

Figure 01g Evolution in Phase Space

evolution of the phase point is more favorable toward the larger "coarse-graining volume" (Figure 01g).

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