“Beyond Boltzmann’s factor: statistical mechanics for interacting particles” by Ralph Chamberlin (Arizona State University)

Wednesday, November 29, 2017 - 4:00pm
Condensed Matter Physics Seminar

Einstein first derived Boltzmann’s factor in 1902 by assuming homogeneous and immediate thermal contact to an effectively infinite heat reservoir. We use experiments, theory, and computer simulations to show that these assumptions are often not met for local fluctuations in systems of interacting particles. We study nonlinear corrections to Boltzmann’s factor guided by 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.

PAB 4-330