1/f noise from the laws of thermodynamics for finite-size fluctuations

Ralph Chamberlin, Derek M. Nasir

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 way to resolve Gibbs' paradox that avoids 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.

Original languageEnglish (US)
Article number012142
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
StatePublished - Jul 30 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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