The following graph, from J. Orban and A. Bellemans, “Velocity-inversion and irreversibility in a dilute gas of hard disks,” Phys. Lett. A, vol. 24, no. 11, pp. 620–621, May 1967, illustrates the solution of Loschmidt paradox.
$$\sin(x)^2+\cos(x)^2=1$$
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