Discrete Modeling: Thermidynamics Based on Shannon Entropy and Discrete States of Molecules

Thermodynamic modeling using the concept of Shannon entropy is a promising approach, especially in the field of describing fluid-phase behavior. This paper introduces the method of discrete modeling, using the ideal-gas model as an illustrative example, and derives a general equation of state. Discrete modeling is based on discrete states of individual molecules. It utilizes the special characteristics of Shannon entropy to model the statistical behavior of systems by applying the maximum entropy principle to its constituents in a straightforward manner. The presented method and the general form of the equation of state thus obtained allow the derivation of equations of states for real fluids. As a novelty, it also allows for the description of the microscopic distribution of the mechanical states of individual molecules. Considering the kinetic states of the particles this includes the Maxwell−Boltzmann distribution, the caloric equation of state, and the heat capacity of the ideal gas.