I will describe two applications of entropy. The first one is relevant to mixing in polymer processing. The other one is relevant to developing a diagnostic tool for low back pain. I analyze the advection of light particles carried by a high viscosity fluid set in motion in a long channel of rectangular cross section and covered by an infinite plate moving at constant velocity. This is a model of a screw extruder, a basic tool for polymer processing. I present an analytic solution of the creeping flow (zero Reynolds number). I analyze the quality and rate of mixing of the particles by calculating Renyi entropies. Surface electromyography (EMG) is used to assess patients with low back pain. In a typical EMG measurement, the voltage is measured every millisecond. The complexity of the EMG time series is characterized using Shannon entropy. The time dependence of the entropy reveals the existence of long time correlations. Furthermore entropy versus time dependence for healthy people is clearly distinct than for low back sufferers.