Studying on Opinion Evolution by Hamilton-Jacobi Equation
  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. 
Chen-Jie Feng, Peng Wang, Jie Huo, Rui Hao and Xu-Ming Wang
physics.soc-ph nlin.AO