Simulation of Fluctuations with 1/f Spectrum

This work presents the results of computer simulation of chaotic motion of elements in models of equilibrium and non-equilibrium systems, which showed that equilibrium fluctuations (white noise) are characteristic of equilibrium systems. In non-equilibrium systems, both equilibrium and non-equilibrium fluctuations are present. Notably, non-equilibrium fluctuations appear at low frequencies and are proportional to 1/f. It is shown that the level of the 1/f component of fluctuations is lower in models where the internal structure is less damaged. In practice, this can be achieved in various ways, for example, by reducing the number of defects in the structure of solid-state elements. An approximation formula for the energy spectrum of fluctuations is presented, where the parameters include the level of equilibrium fluctuations (thermal noise for electronic components) and the degree of deviation from the equilibrium state of the system under study, expressed through the relaxation time. Therefore, the proposed formula can be applied to approximate 1/f-type fluctuations in any real system – electrical fluctuations, biological fluctuations, geophysical fluctuations, etc. The approximation formula allows us to estimate the fluctuation level in the low-frequency range.