Data from: A statistical mechanics framework for constructing non-equilibrium thermodynamic models

<p><span>Far-from-equilibrium phenomena are critical to all natural and engi</span><span>neered systems, and essential to biological processes responsible </span><span>for life. For over a century and a half, since Carnot, Clausius, Maxwell, </span><span>Boltzmann, and Gibbs, among many others, laid the foundation for </span><span>our understanding of equilibrium processes, scientists and engineers </span><span>have dreamed of an analogous treatment of non-equilibrium systems. </span><span>But despite tremendous efforts, a universal theory of non-equilibrium </span><span>behavior akin to equilibrium statistical mechanics and thermodynam</span><span>ics has evaded description. Several methodologies have proved their </span><span>ability to accurately describe complex non-equilibrium systems at </span><span>the macroscopic scale, but their accuracy and predictive capacity is </span><span>predicated on either phenomenological kinetic equations fit to mi</span><span>croscopic data, or on running concurrent simulations at the particle </span><span>level. Instead, we provide a framework for deriving stand-alone macro</span><span>scopic thermodynamics models directly from microscopic physics </span><span>without fitting in overdamped Langevin systems.</span> <span>The only neces</span><span>sary ingredient is a functional form for a parameterized, approximate </span><span>density of states, in analogy to the assumption of a uniform density </span><span>of states in the equilibrium microcanonical ensemble. We highlight </span><span>this framework's effectiveness by deriving analytical approximations </span><span>for evolving mechanical and thermodynamic quantities in a model of </span><span>coiled-coil proteins and double stranded DNA, thus producing, to the </span><span>authors' knowledge, the first derivation of the governing equations for </span><span>a phase propagating system under general loading conditions without </span><span>appeal to phenomenology. The generality of our treatment allows </span><span>for application to any system described by Langevin dynamics with </span><span>arbitrary interaction energies and external driving, including colloidal </span><span>macromolecules, hydrogels, and biopolymers.</span></p>