The bundle of -curves Its concentration curve

The bundle of H-curves lie concentration curve. Let us consider a distribution ZA of state with a relatively high H(Za) at tA. Let us find the corresponding Z -star in the T-space (cf. Section 12b). The continuum of the motions of all the points in the star produces a bundle of //-curves in the (t, H) plane which radiate out of a point t=tA,H=H(Z)A. We make the following assertions about its behavior 140 

Let us collect these values 3Ci, 3Cj, 3C , into a discrete set of points and call this briefly the concentration curve of the bundle. Then we assert in addition  

The curve of the H-theorem. In the context of the formulation which we have used since Section 9, the Slosazahlansatz (Section 3b), and with it the whole H-theorem, are still a meaningless computational scheme.14 The initial distribution ZA defines a new Z for the end of each successive interval At. Let us denote these distributions by Zi, Zj, . One thus obtains in addition to the previous //-curves a new //-sequence, which is discrete (the spacing of the abscissa At) and which decreases monotonically (cf. Section 6). We call this the curve of the //-theorem.  

This generates a statistical formulation of the H-theorem through the following assertion, which is again unproved  

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