Spatial structure and stability based on random walks

A general expression for a recursion formula which describes a random walk with coupled modes is given. In this system, the random walker is specified by the jumping probabilities P⁺ and P^– which depend on the modes. The transition probability between the modes is expressed by a jumping probabilityR ^(ij) (orr _ij). With the aid of this recursion formula, spatial structures of the steady state of a coupled random walk are studied. By introducing a Liapunov function and entropy, it is shown that the stability condition for the present system can be expressed as the principle of the extremum entropy production.On leave of absence from Tohoku University, Department of Applied Science, Faculty of Engineering, Sendai, 980 Japan.