A family of techniques in physics known as statistical mechanics is useful for describing the macroscopic properties of materials composed of a large (Avogadro's # ≈ 10²⁴) number of atoms. This talk applies the same approach to the analysis of big data problems. The initial problem examined is that of classification, specifically binary hypothesis testing, in the big data, high dimensional scenario. The lessons learned from the binary hypothesis testing problem are extended to other signal processing paradigms.