A Field Theory of Entropy

Starting from an argument on the impossibility of emergence of temperature within current physics, we propose to take temperature as a fundamental property of matter, with rest energy of $E=2k_B T$. As an inductive consequence, this fundamental property of matter must produce a field of entropy according to the equation $\square S=-\frac{\kappa}{2}k_B^2\theta$, where $\kappa=8\pi G /c^4$ is Einstein's constant, and $\theta$ temperature density per unit volume.

Design of intrinsically disordered proteins that undergo phase transitions with lower critical solution temperatures

Many naturally occurring elastomers are intrinsically disordered proteins (IDPs) built up of repeating units and they can demonstrate two types of thermoresponsive phase behavior. Systems characterized by lower critical solution temperatures (LCST) undergo phase separation above the LCST whereas systems characterized by upper critical solution temperatures (UCST) undergo phase separation below the UCST. There is congruence between thermoresponsive coil-globule transitions and phase behavior whereby the theta temperatures above or below which the IDPs transition from coils to globules serve as useful proxies for the LCST / UCST values. This implies that one can design sequences with desired values for the theta temperature with either increasing or decreasing radii of gyration above the theta temperature. Here, we show that the Monte Carlo simulations performed in the so-called intrinsic solvation (IS) limit version of the temperature-dependent ABSINTH implicit solvation model, yields a useful heuristic for discriminating between sequences with known LCST versus UCST phase behavior. Accordingly, we use this heuristic in a supervised approach, integrate it with a genetic algorithm, combine this with IS limit simulations, and demonstrate that novel sequences can be designed with LCST phase behavior. These calculations are aided by direct estimates of temperature dependent free energies of solvation for model compounds that are derived using the polarizable AMOEBA forcefield. To demonstrate the validity of our designs, we calculate coil-globule transition profiles using the full ABSINTH model and combine these with Gaussian Cluster Theory calculations to establish the LCST phase behavior of designed IDPs.

Viscosity Measurements of Dilute Poly(2-ethyl-2-oxazoline) Aqueous Solutions Near Theta Temperature Analyzed within the Joint Rouse-Zimm Model

The steady-state shear viscosity of low-concentrated Poly(2-ethyl-2-oxazoline) (PEOX) aqueous solutions is measured near the presumed theta temperature using the falling ball viscometry technique. The experimental data are analyzed within the model that joins the Rouse and Zimm bead-spring theories of the polymer dynamics at the theta condition, which means that the polymer coils are considered to be partially permeable to the solvent. The polymer characteristics thus depend on the draining parameterhthat is related to the strength of the hydrodynamic interaction between the polymer segments. The Huggins coefficient was found to be 0.418 at the temperature 20°C, as predicted by the theory. This value corresponds toh= 2.92, contrary to the usual assumption of the infiniteh. This result indicates that the theta temperature for the PEOX water solutions is 20°C rather than 25°C in the previous studies. The experimental intrinsic viscosity is well described coming from the Arrhenius equation for the shear viscosity.