Abstract: A type of model with discrete variables is proposed. Based on the model and the maximum entropy principle, applications of statistical physics method are discussed in thermodynamical systems. The model is able to be extended to other non-physical systems composed of lots of elements, such as financial system and social production system. The probability distribution function obtained from the maximum entropy principle can be applied to equilibrium and non-equilibrium stationary system with the same boundary.

Key words: group, maximum entropy principle, Shannon entropy, non-equilibrium stationary state