Verbal communication is companied by rich non-verbal signals. The usage of gestures, poses, and facial expressions facilitates the information transmission in verbal channel. However, few computational studies have explored the non-verbal channels with finer theoretical lens. We extract gesture representations from monologue video data and train neural sequential models, in order to study the degree to which non-verbal signals can effectively transmit information. We focus on examining whether the gestures demonstrate the similar pattern of entropy rate constancy (ERC) found in words, as predicted by Information Theory. Positive results are shown to support the assumption, which leads to the conclusion that speakers indeed use simple gestures to convey information that enhances verbal communication, and the production of non-verbal information is rationally organized.