In this paper we derive a statistical formula for entropy production rate,namely the law of entropy increase in 6N- and 6-dimensional phase spaces. The exp ression is P=kD(Δqθ)2,which means the entropy produc tion rate P eq ual to the product of diffusion coefficient D,the mean square value of the spac e gradient of the percentage departure from equilibrium θ and Boltzmann constan t k. It shows that the macroscopic entropy production in a nonequilibrium system is caused by spatially stochastic and inhomogeneous departure from equilibrium of the number density of micro-states. As its application, we use this formula t o investigate three nonequilibrium physical topics: free expansion of a gas, Bro wnian motion, and the deformation and fracture of solids. The expressions for th eir entropy production,and the first and second time rates are presented. A new physical inference that the change of micro-structure within the system during a n irreversible process is inhomogeneous has been drawn and confirmed. We also ca lculate the entropy production rate in the stationary state, derive a special fo rmula, present the actual expressions of two examples: directed atomic diffusion and molecular motor. All these theoretical results are either in agreement with experiment or reasonable in physics.
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