Labour productivity distribution (dispersion) is studied within the framework of statistical physics and the result is compared with the outcome of the empirical analysis. Superstatistics is presented as a natural theoretical framework for the productivity distribution. The demand index κ is proposed within this framework as a new business index. Productivity analysis is made on the Japanese data covering small-to-medium to large firms from 1996 to 2006 and the power-law for both firms and workers is established. The demand index κ is evaluated in the manufacturing sector. A new discovery is reported for the nonmanufacturing (service) sector, which calls for an expansion of the superstatistics framework to include the negative temperature range.