| # Power laws Consider a physical process which has inputs , , and a scalar output . Inputs and output are physical, positive quantities, such as volume, height, or temperature. In many cases, we can (at least empirically) describe such physical processes by power laws, which are non-linear models of the form where , and the coefficients , are real numbers. For example, the relationship between area, volume and size of basic geometric objects; the Coulomb law in electrostatics; birth and survival rates of (say) bacteria as functions of concentrations of chemicals; heat flows and losses in pipes, as functions of the pipe geometry; analog circuit properties as functions of circuit parameters; etc. The relationship is not linear nor affine, but if we introduce the new variables , , , then the above equation becomes an affine one: where . See also: Fitting power laws to data.