  Recently, A.N. Gorban presented a rich family of universal Lyapunov functions
for any linear or non-linear reaction network with detailed or complex balance.
Two main elements of the construction algorithm are partial equilibria of
reactions and convex envelopes of families of functions. These new functions
aimed to resolve "the mystery" about the difference between the rich family of
Lyapunov functions (f-divergences) for linear kinetics and a limited collection
of Lyapunov functions for non-linear networks in thermodynamic conditions. The
lack of examples did not allow to evaluate the difference between Gorban's
entropies and the classical Boltzmann--Gibbs--Shannon entropy despite of
obvious difference in their construction. In this paper, results of A.N. Gorban
are briefly reviewed, and these functions are analysed and compared for several
mechanisms of chemical reactions. The level sets and dynamics along the kinetic
trajectories are analysed. The most pronounced difference between the new and
classical thermodynamic Lyapunov functions was found far from the partial
equilibria, whereas when some fast elementary reactions became close to
equilibrium then this difference decreased and vanished in partial equilibria.
