  A physical description of an opinion evolution is conducted based on the
Hamilton-Jacobi equation derived from a generalized potential and the
corresponding Langevin equation. The investigation mainly focuses on the
heterogeneities such as age, connection circle and overall quality of the
participants involved in the opinion exchange process. The evolutionary
patterns of opinion can be described by solution of the Hamilton-Jacobi
equation, information entropy. The results show that the overall qualities of
the participants play critical roles in forming an opinion. The higher the
overall quality is, the easier the consensus can reach. The solution also
demonstrates that the age and the connection circle of the agents play equally
important roles in forming an opinion. The essence of the age, overall quality,
and connection circle corresponds to the maturity of thought (opinion inertia),
reason and intelligence, influence strength of the environment, respectively.
So the information entropy distributes in the phase planes (two variable
combinations out of the three---age, connection circle and overall quality)
exhibit the evolution rules of an opinion.
