熵产生率公式及其应用

导出了6N维和6维相空间的熵产生率，即熵增加定律的一个统计公式：P=kD(Δ_{qθ)²，即熵产生率P等于扩散系数D、离开平衡率θ的空间梯度平方的平均值与Boltzm ann常数k 三者之乘积.指明非平衡系统的宏观熵产生是由其微观状态数密度在空间随机地不均匀离开 平衡引起的.作为公式的应用,研究了气体自由膨胀、布朗运动及固体变形和断裂三个非平衡 态课题，给出了它们的熵产生及其一次和二次时间变化率，得到了不可逆过程的系统内对应 的微观结构变化是不均匀的推论.进而导 关键词： 熵产生率 微观状态数密度 离开平衡率 随机扩散}

On the formula for entropy production rate

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(Δ_qθ)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.