Entropy and entropy production in some applications

•Entropy and entropy production are combined into a single quantity to determine the stationary state.•The thermal conductivity and the viscosity of a dilute gas are derived in a competition method.•Atomic diffusion and the Nernst–Einstein relation are studied.

By using entropy and entropy production, we calculate the steady flux of some phenomena. The method we use is a competition method, SS/τ+σ=maximum, where SSSS is system entropy, σσ is entropy production and ττ is microscopic interaction time. System entropy is calculated from the equilibrium state by studying the flux fluctuations. The phenomena we study include ionic conduction, atomic diffusion, thermal conduction and viscosity of a dilute gas.