1/f Noise from the Laws of Thermodynamics for Finite-Size Fluctuations

TL;DR

This paper demonstrates that 1/f noise in finite systems can be explained by extending thermodynamic laws to include local entropy effects, aligning with observed spectral behaviors in metals and nanoscale systems.

Contribution

It introduces a nonlinear correction to Boltzmann's factor that accounts for local entropy, providing a thermodynamic basis for 1/f noise in finite-size fluctuations.

Findings

The model matches the temperature dependence of spectral-density exponents in metals.

It reproduces non-Gaussian fluctuations observed in nanoscale systems.

The correction maintains maximum entropy and energy conservation in equilibrium fluctuations.

Abstract

Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local alignment entropy to all orders. We show that this nonlinear correction maintains maximum entropy during equilibrium fluctuations. Indeed, as with the usual resolution of Gibbs' paradox that avoids net entropy reduction during reversible processes, the correction yields the statistics of indistinguishable particles. The correction also ensures conservation of energy if an instantaneous contribution from local entropy is included. Thus, a common mechanism for 1/f noise comes from assuming that finite-size fluctuations strictly obey the laws of thermodynamics, even in small parts of a large system. Empirical evidence for the model comes from its ability to match the measured temperature dependence of the spectral-density exponents in several metals, and to show non-Gaussian fluctuations characteristic of nanoscale systems.