Reducing low-frequency noise during reversible fluctuations

The noise from most materials exhibits a power-spectral density that tends to diverge as S(f) ∝ 1/f at low frequencies, f. A fundamental mechanism for this 1/f noise comes from the thermodynamics of small systems applied to reversible fluctuations of nanometer-sized regions inside bulk samples. Here this “nanothermodynamics” is used to derive a nonlinear correction to Boltzmann’s factor. Specifically: Boltzmann’s factor comes from the first-order (linear) derivative of entropy with respect to energy, whereas the nonlinear correction comes from higher-order terms. The nonlinear correction is applied to Monte Carlo simulations of small regions in the Ising model, yielding a low-frequency crossover to white noise that keeps the power-spectral density finite as f → 0. It is shown that the low-frequency noise in the model is reduced by reducing the size of the regions.