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

Some dividing cells sense their shape by becoming polarized along their long axis. Cell polarity is controlled in part by polarity proteins, like Rho GTPases, cycling between active membrane-bound forms and inactive cytosolic forms, modeled as a “wave-pinning” reaction-diffusion process. Does shape sensing emerge from wave pinning? We show that wave pinning senses the cell’s long axis. Simulating wave pinning on a curved surface, we find that high-activity domains migrate to peaks and troughs of the surface. For smooth surfaces, a simple rule of minimizing the domain perimeter while keeping its area fixed predicts the final position of the domain and its shape. However, when we introduce roughness to our surfaces, shape sensing can be disrupted, and high-activity domains can become localized to locations other than the global peaks and valleys of the surface. On rough surfaces, the domains of the wave-pinning model are more robust in finding the peaks and troughs than the minimization rule, although both can become trapped in steady states away from the peaks and valleys. We can control the robustness of shape sensing by altering the Rho GTPase diffusivity and the domain size. We also find that the shape-sensing properties of cell polarity models can explain how domains localize to curved regions of deformed cells. Our results help to understand the factors that allow cells to sense their shape—and the limits that membrane roughness can place on this process. 

“Viscosity is the most ubiquitous dissipative mechanical behavior” (Maugin, 1999). Despite its ubiquity, even for those systems where the mechanisms causing viscous and other forms of dissipation are known there are only a few quantitative models that extract the macroscopic rheological response from these microscopic mechanisms. One such mechanism is the stochastic breaking and forming of bonds which is present in polymer networks with transient cross-links, strong inter-layer bonding between graphene sheets, and sliding dry friction. In this paper we utilize a simple yet flexible model to show analytically how stochastic bonds can induce an array of rheological behaviors at the macroscale. We find that varying the bond interactions induces a Maxwell-type macroscopic material behavior with Newtonian viscosity, shear thinning, shear thickening, or solid like friction when subjected to shear at constant rates. When bond rupture is independent of the force applied, Newtonian viscosity is the predominant behavior. When bond breaking is accelerated by the applied force, a shear thinning response becomes most prevalent. Further connections of the macroscopic response to the interaction potential and rates of bonding and unbonding are illustrated through phase diagrams and analysis of limiting cases. Finally, we apply this model to polymer networks and to experimental data on “solid bridges” in polydisperse granular media. We imagine possible applications to material design through engineering bonds with specific interactions to bring about a desired macroscopic behavior. 

Abstract The solution rheology of a fully synthetic, monodisperse mucin that mimics the glycosylated domains of natural mucins, poly(β‐Gal‐Thr)₂₂, is studied to systematically explore relationships between polymer structure, solution conditions, and rheological properties. Using standard cone‐plate rheometry, shear thinning is observed over a range of concentrations, with an apparent yield stress—typical for gels—evident at the highest concentrations. This is surprising given the dilute, weakly interacting nature of the solutions and the lack of observable structure in cryogenic electron microscopy and particle tracking microrheology. However, interfacial rheometry demonstrates that the gel‐like behavior is attributable to a thin structured layer at the air–water interface, without any bulk gelation. This is attributed to an interfacial layer formed by inter‐mucin H‐bonds that yields when sheared. A computational model using kinetic Monte Carlo (kMC) simulations qualitatively reproduces the yield stress response of such a network through an intermolecular bonding potential. An analytical model of stochastic bond formation and breaking, validated by the kMC simulations, demonstrates that having multiple bonding sites per mucin with a force‐dependent debonding rate aligns with experiments, consistent with intermolecular interactions for other mucin proteins. This suggests that in mucin solutions, gelation may begin at the air–water interface, and emphasizes the need for multitechnique validation when exploring structural cues of mucus gelation through rheometry.