Estimating thermodynamic quantities far from equilibrium

In this thesis, a novel framework for constructing macroscopic thermodynamic models arbitrarily far away from equilibrium is presented. This method, rooted in an approximation of the fundamental thermodynamic quantities from stochastic thermodynamics, establishes a connection between microscopic particle systems governed by overdamped Langevin dynamics at a well defined temperature and popular non-equilibrium thermodynamics models used at the macroscopic scale, namely thermodynamics with internal variables and the so-called GENERIC framework. We refer to this new framework as Stochastic Thermodynamics with Internal Variables (STIV). One need only specify a parameterized approximation to the system’s density of states, and the STIV framework provides both dynamic and thermodynamic equations without additional phenomenological assumptions or the need to fit to data. The various applications laid out within, including those of the unfolding of coiled-coil proteins, and protein diffusion on DNA, demonstrate both the framework’s flexibility and accuracy. Additionally, in the final chapter of this thesis, we highlight how a stochastic model of cross-link bonding can be tuned to produce a wide range of rheological behavior. In particular, for bonding energies with quadratic minima and assuming bond breaking is accelerated due to applied force (as is most often true), the stochastic bonds model predicts a shear thinning response to applied shearing. Finally, Kinetic Monte Carlo simulations and maximum likelihood estimation of model parameters are used to study bond energies and dissipation in solid bridges.