  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.
