Arizona State University
Equilibrium fluctuations, heterogeneous response, and 1/f noise from local transient effects in thermodynamics
Some remarkably universal empirical formulas are used to characterize the primary response of complex systems. Stretched-exponential relaxation has been used since 1854 for time-dependent response, non-classical critical scaling has been used since 1893 for temperature-dependent behavior, and 1/f noise has been used since 1925 for frequency-dependent fluctuations. I will describe a common physical foundation for all these formulas. The ideas are based on “nanothermodynamics,” where nanometer-sized systems couple to a local thermal bath from the surrounding ensemble of similarly small systems. The mechanism can be attributed to strict adherence to the laws of thermodynamics: non-extensive energy is conserved by including Hill’s subdivision potential, and maximum entropy is maintained by transferring information to the surrounding bath. Alternatively the mechanism may involve the statistics of indistinguishable particles for equivalent states. I will emphasize how using these ideas, standard theories and simulations yield the empirical formulas, plus deviations from the formulas that often match measured behavior. Finally, I plan to present some recent results showing that molecular dynamics simulations of several models exhibit anomalous fluctuations in the local energy. Specifically, small systems containing 1-1000 atoms inside much larger simulations have energy fluctuations that differ significantly from a fluctuation-dissipation relation, sometimes by an order of magnitude or more.