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In this paper we develop the concept of information transfer between theBorel-measurable sets for a dynamical system described by a measurable spaceand a non-singular transformation. The concept is based on how Shannon entropyis transferred between the measurable sets, as the dynamical system evolves. Weshow that the proposed definition of information transfer satisfies the usualnotions of information transfer and causality, namely, zero transfer andtransfer asymmetry. Furthermore, we show how the information transfer measurecan be used to classify ergodicity and mixing. We also develop thecomputational methods for information transfer computation and apply theframework for optimal placements of actuators and sensors for control ofnon-equilibrium dynamics.

Information Transfer in Dynamical Systems and Optimal Placement of Actuators and Sensors for Control of Non-equilibrium Dynamics