Boltzmann’s factor was first derived by Einstein in 1902 assuming macroscopic thermodynamics for homogeneous thermal coupling to an effectively infinite heat reservoir. We use experiments, theory, and computer simulations to show that these assumptions are not met for local fluctuations in systems of interacting particles. We study nonlinear corrections to Boltzmann’s factor based on Terrell Hill’s “nanothermodynamics,” where nanometer-sized systems couple to a local bath of similarly small systems. The corrections can be attributed to strict adherence to the laws of thermodynamics: non-extensive energy is conserved by including Hill’s subdivision potential, while maximum entropy is maintained by transferring information to the local bath. Alternatively the mechanism may involve the statistics of indistinguishable particles for equivalent states. One result is a common physical foundation for several empirical formulas that have long been used to characterize the primary response of complex systems, including the stretched-exponential function for time-dependent relaxations, non-classical critical scaling for temperature-dependent susceptibilities, and 1/f noise for frequency-dependent fluctuations. I will emphasize how nonlinear corrections to the Metropolis algorithm 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 1-2000 atoms inside much larger simulations have energy fluctuations that differ significantly from a fluctuation-dissipation relation, sometimes by an order of magnitude or more.
Ralph Chamberlin received his undergraduate degree in physics from the University of Utah, working with Orest Symko. He received his PhD in 1984 from the University of California, Los Angeles, working with Ray Orbach. He spent two years as a post-doc at the University of Pennsylvania working with Paul Chaikin. He joined Arizona State University in 1986. His career has shifted between experiments, theory, and computer simulations. He has been involved in developing and interpreting stretched-exponential relaxation for spin glasses, non-resonant spectral hole burning for supercooled liquids, and nanothermodynamics for the thermal and dynamics properties of complex systems on the scale of nanometers.