This study investigates heart wall motion abnormality detection with an information theoretic measure of heart motion based on the Shannon's differential entropy (SDE) and recursive Bayesian filtering. Heart wall motion is generally analyzed using functional images which are subject to noise and segmentation inaccuracies, and incorporation of prior knowledge is crucial in improving the accuracy. The Kalman filter, a well known recursive Bayesian filter, is used in this study to estimate the left ventricular (LV) cavity points given incomplete and noisy data, and given a dynamic model. However, due to similarities between the statistical information of normal and abnormal heart motions, detecting and classifying abnormality is a challenging problem which we proposed to investigate with a global measure based on the SDE. We further derive two other possible information theoretic abnormality detection criteria, one is based on Rényi entropy and the other on Fisher information. The proposed method analyzes wall motion quantitatively by constructing distributions of the normalized radial distance estimates of the LV cavity. Using 269 x 20 segmented LV cavities of short-axis magnetic resonance images obtained from 30 subjects, the experimental analysis demonstrates that the proposed SDE criterion can lead to significant improvement over other features that are prevalent in the literature related to the LV cavity, namely, mean radial displacement and mean radial velocity.