  In the present study, the information entropy for smoluchowski coagulation
equation is proposed based on the statistical physics. and the normalized
particle size distribution is a log-normal function at equilibrium from the
principle of maximum entropy and moment constraint. the parameters in the
particle size distribution are determined as simple constants, the result
reveals that the assumption that algebraic mean volume be unit in
self-preserving hypothesis is reasonable. based on the present definition of
the information entropy, the cercignani conjecture holds naturally for
smoluchowski coagulation equation. Together with the fact that the conjecture
is also true for Boltzmann equation, cercignani conjecture holds for any
two-body collision systems, which will benefit the understanding of Brownian
motion and molecule kinematic theory, such as the stability of the dissipative
system, and the mathematical theory of convergence to thermodynamic
equilibrium.
