Application of the concept of local equilibrium to solve the Fokker-Planck equation

A method for speeding up the classical Monte Carlo method is presented. The proposed method is based on the observation that the Boltzmann transition probability and the concept of local thermodynamic equilibrium give rise to an initial state of maximum entropy. This state can be modified by using internal structural information of the system. In classical thermodynamic models, internal structures of systems are not taken into account. It is proposed to use the Dempster-Shafer theory. Starting from local thermodynamic equilibrium (local symmetry), the proposed algorithm computes the new distribution over subsystems, resulting in a non-uniform distribution and in symmetry breaking. For the more general case, an initial local distribution that is induced by different symmetries can be assumed. From this, the global distribution which breaks the local symmetry can be calculated