Maximizing entropy change for nonequilibrium systems

We propose maximizing the change of thermodynamic entropy in order to obtain the probability distributions for nonequilibrium systems in steady or stationary evolution. Arguments are forwarded to support this approach. A path information leading to Kolmogorov-Sinai entropy is defined for an ensemble of possible trajectories between two points in phase space. It is shown that the maximization of this information leads to the most probable paths which minimize action. This result suggests a statistical interpretation of the principle of least action. In the second part of this work, the principle of maximal change of thermodynamic entropy is applied to the nonequi-librium systems evolving in fractal or hierarchic phase space thanks to the relative entropy change given by R = i p i − i p q i , where q is in general a real parameter characterizing the fractal features of the phase space and the sign of entropy production. It is shown that the maximization of |R| is useful for many chaotic systems. A possible nonequilibrium thermodynamics is discussed in connection with Havrda-Charvat-Tsallis entropy S q = − R 1−q .