The study of human mobility patterns is a crucially important research field for its impact on several socio-economic aspects and, in particular, the measure of regularity patters of human mobility can provide a across-the-board view of many social distancing variables in epidemics such as: human movement trends, physical interpersonal distances and population density. We will show that the notion of information entropy is also strongly related to demographic and economic trends by the use and analysis of real-time data. In the present research paper we address three different problems. First, we provide an evidence-based analytical approach which relates the human mobility patterns, social distancing attitudes and population density, with entropic measures which depict for erraticity of human contact behaviors. Second, we investigate the correlations between the aggregated mobility and entropic measures versus five external economic indicators. Finally, we show how entropic measures represents a useful tool for testing the limitations of typical assumptions in epidemiological and mobility models.