Spectral 1/<i>f</i>noise derived from extremized physical information

Abstract

We consider the evolution of a temporal signal X(t) that is an intrinsic random field of order zero. In the sense of a certain measurement-estimation experiment, the state of disorder of X(t) should increase toward an equilibrium state. The disorder of X(t) is measured by its ``physical information'' scrI, and the equilibrium state is determined by the condition that scrI be an extremum. The equilibrium state is shown to have a power spectrum S(\ensuremath{\omega}) of the form ${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\alpha}}}$,1\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}2, that of 1/f noise.