The origin of 1/f fluctuations and scale transformations of time series at nonequilibrium phase transitions

Investigations of the dynamics of heat and mass transfer show that in crisis and transient conditions one can observe high-energy fluctuations with a power spectrum inversely proportional to the frequency (flicker or 1/f fluctuations). Such a spectrum presupposes energy transient from high to lower frequency modes and the possibility of large-scale catastrophic events in a system. Theory shows that such fluctuations arise in a system owing to the simultaneous progress of interacting phase transitions in the presence of a white noise of sufficient intensity. The distributions functions of fluctuations during scale transformations of a system of stochastic equations describing the 1/f noise generations have been investigated. It is shown that the Gaussian distributions of a random process with a 1/f spectrum under a roughness of a scale change to exponential distribution characteristic of the statistics of extreme events. The probability of such events should be taken into account in predicting the stability of different heat transfer regimes.