  Boltzmann's H-Theorem, formulated 150 years ago in terms of H-function that
also bears his name, is one of the most celebrated theorems of science and
paved the way for the development of nonequilibrium statistical mechanics.
Nevertheless, quantitative studies of the H-function, denoted by H(t), in
realistic systems are relatively scarce because of the difficulty of obtaining
the time-dependent momentum distribution analytically. Also, the earlier
attempts proceeded through the solution of Boltzmann's kinetic equation, which
was hard. Here we investigate, by direct molecular dynamics simulations and
analytic theory, the time dependence of H(t). We probe the sensitivity of
nonequilibrium relaxation to interaction potential and dimensionality by using
the H-function H(t). We evaluate H(t) for three different potentials in all
three dimensions and find that it exhibits surprisingly strong sensitivity to
these factors. The relaxation of H(t) is long in 1D, but short in 3D. We
obtain, for the first time, a closed-form analytic expression for H(t) using
the solution of the Fokker-Planck equation for the velocity space probability
distribution and compare its predictions with the simulation results.
Interestingly, H(t) is found to exhibit linear response when vastly different
initial nonequilibrium conditions are employed. The oft-quoted relation of
H-function with Clausius's entropy theorem is discussed.
