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Center for Nonlinear Studies |
It is well-known that classical mechanics must be modified to accurately treat interatomic interactions; not so well-known is the fact that standard thermodynamics must also be changed on a similar length scale. The theory of small-system thermodynamics was originally developed by Terrell Hill to describe isolated nanoparticles and individual molecules, but we find that this “nanothermodynamics†also provides a basis for understanding nanometer-sized fluctuations inside bulk materials. One result is a nonlinear correction to Boltzmann’s factor. The mechanism may be attributed to finite-size effects in the laws of thermodynamics: total energy is conserved by including Hill’s subdivision potential, net entropy is maximized by coupling to the thermal bath, and/or similar states are treated using the statistics of indistinguishable particles. The nonlinear correction provides a common basis for several empirical formulas that have been used to characterize the dynamics of complex systems, including stretched-exponential relaxation, super-Arrhenius activation, non-classical critical scaling, and 1/f noise. I will emphasize how specific models based on nanothermodynamics yield these simple formulas, plus deviations from the formulas that match the measured behavior in many materials.
Host: Sebastian Deffner