Thermodynamic geometry of supercooled water

Abstract

The thermodynamic curvature scalar R is evaluated for supercooled water with a two-state equation of state correlated with the most recent available experimental data. This model assumes a liquid-liquid critical point. Our investigation extends the understanding of the thermodynamic behavior of R considerably. We show that R diverges to -∞ when approaching the assumed liquid-liquid critical point. This limit is consistent with all of the fluid critical point models known so far. In addition, we demonstrate a sign change of R along the liquid-liquid line from negative near the critical point to positive on moving away from the critical point in the low density "ice-like" liquid phase. We also trace out the Widom line in phase space. In addition, we investigate increasing correlation length in supercooled water and compare our results with recent published small angle x-ray scattering measurements.

Thermodynamic metric geometry of the two-state ST2 model for supercooled water

“…In our present study, the geometric structure of the ST2 model for supercooled water is analyzed based on the TSEOS developed by Holten et al [54], which models well the properties of real water [7,31]. Two versions of the TSEOS have been developed [54], a mean-field (MF) description and a so-called crossover (CO) approach, accounting for critical order-parameter fluctuations.…”

“…We recently extended these geometric ideas into the metastable water regime [7]. By applying a two-state equation of state (TSEOS), developed by Holten et al [31], a dramatically decreasing R, to −∞ at the postulated LLCP, was found on cooling into the metastable liquid state [7]. On the LDL side of the LLPT line, organized ice-like structures led to positive R, whereas the HDL side shows only negative R. Positive R in the LDL state appeared because tetragonal ice-like structures generally take up more space than the more disorganized HDL states.…”

“…Based on simulation studies [60,61] both versions have been fit to a mean-field (MF) thermodynamic picture, and MF has been augmented by a crossover procedure to critical behavior [54]. In this paper we compute R for the MF pictures, ST2(I-MF), and ST2(II-MF), both of which have non-zero critical pressures, as opposed to the model we employed in our previous study [7] that has its second critical point at zero pressure.…”

Thermodynamic geometry of strongly interacting matter

“…(14) and Eqs. (17)(18)(19)(20)(21)(22)(23). The black curves are based on lattice data with the condition n S = n Q = 0 (or equivalent for the isospin symmetric limit), whereas the red ones are for n S = 0 and n Q /n B = 0.4.…”

Antiferromagnetic Ising Model in the Framework of Riemannian Geometry

“…Riemannian geometric theory of thermodynamics and statistical mechanics is nowadays successfully applied in diverse research areas [1][2][3][4][5][6][7][8][9]. At the beginning, these applications are limited to simple and well-known spin models.…”