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Register a new user1/f Noise from the Laws of Thermodynamics for Finite-Size Fluctuations
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Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmanns factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmanns 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.
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This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are briefly sketched. The finite size scaling method is described. Recent results for the critical exponents of the different symmetry classes are summarised. The importance of corrections to scaling are emphasised. A comparison with experiment is made, and a direction for future work is suggested.
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