Information Geometry on Complexity and Stochastic Interaction

Abstract

Interdependencies of stochastically interacting units are usually quantified by the Kullback-Leibler divergence of a stationary joint probability distribution on the set of all configurations from the corresponding factorized distribution. This is a spatial approach which does not describe the intrinsically temporal aspects of interaction. In the present paper, the setting is extended to a dynamical version where temporal interdependencies are also captured by using information geometry of Markov chain manifolds.

Keywords

• stochastic interaction
• complexity
• information geometry
• Kullback-Leibler divergence
• separability
• Markov chains
• random fields