Determination of preferential exponent α in random processes with a 1∕fα power spectrum

The stability of fluctuation processes with 1∕fα power spectra in systems of stochastic equations simulating coupled phase transitions has been analyzed with the use of the maximum information entropy principle. It is shown that in the class of processes described by a nonpotential system of model equations fluctuations with a 1/f power spectrum, i.e. with the exponent α=1, are preferential, Preferential for the class of potential systems under consideration are fluctuations with a 1∕fα spectrum at α=1.3. The spectral entropy of the random processes has been calculated. Calculation of the spectral entropy makes it possible to investigate the stability of random processes directly from the power spectra, without calculating the probability density functions. The dependence of the spectral entropies on the amplitude of white noise has a minimum whose position corresponds to the critical behavior.