Fuzzy dynamics as an alternative to statistical mechanics

We propose a description of continuous evolution of systems with uncertainty based on min or product t-norms of fuzzy logic. We show that the dynamics has a Hamiltonian form in the extended state space composed from “physical” and “information” components if the min t-norm is used. This description is useful when available information on a system behavior is mainly ordinal and not numerical. If the product t-norm is used, the dynamics on a continuous universe is similar to the dynamics of stochastic processes , but the probability distribution is replaced by a possibility density. We show, that such replacement leads to an essential extension of the stochastic process theory. The differential equation of evolution of the possibility density cover most basic dynamics equations in physics.