Paths towards equilibrium in molecular systems: The case of water

A. Gijón, A. Lasanta, and E. R. Hernández

Phys. Rev. E 100, 032103 – Published 3 September 2019

Abstract

We consider the problem of how a condensed molecular system approaches equilibrium, focusing on the particular case of water. We show, by means of extensive molecular dynamics simulations, that the existence of different types of degrees of freedom affects the dynamics of equilibration, and this influence is made most obvious in the system's temperature. When equipartition of energy does not hold in the initial, nonequilibrium state, the instantaneous temperature can be up to a few degrees lower than that observed under equipartition conditions, resulting in a Mpemba-like effect. Though our study considers water in particular, our findings apply more generally to condensed molecular systems.

Received 14 May 2019

DOI:https://doi.org/10.1103/PhysRevE.100.032103

Physics Subject Headings (PhySH)

Nonequilibrium & irreversible thermodynamics Thermodynamics

Water

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Gijón¹, A. Lasanta^2,*, and E. R. Hernández ^1,†

¹Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Campus de Cantoblanco, 28049 Madrid, Spain
²G. Millán Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Leganés, Spain

^*Present address: Departamento de Álgebra. Facultad de Educación, Econonía y Tecnología de Ceuta, Universidad de Granada, Cortadura del Valle, s/n. E-51001 Ceuta, Spain; alasanta@ugr.es
^†Eduardo.Hernandez@csic.es

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Issue

Vol. 100, Iss. 3 — September 2019

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Images

Figure 1
(a) Evolution of the total, translational, and rotational kinetic energy towards equipartition for liquid TIP4P water; at the start of this simulation, all the kinetic energy was in translational modes; (b) evolution of the temperature in three different situations: (1) starting from equipartition, (2) kinetic energy initially only in translational modes [the case displayed in panel (a)], and (3) kinetic energy initially in rotational modes only [the reverse case of that shown in panel (a)]. (c) Translational velocity autocorrelation function (tVAF) of liquid TIP4P water at 350 K. VAFs of Cartesian velocity components are shown in black, while those of velocity components in the molecular frame are shown in blue, red, and green; the disposition of the molecular frame is indicated by the inset, in which each axis is colored to accord with the corresponding tVAF component. (d) Rotational velocity autocorrelation function (rVAF) of liquid TIP4P water at 350 K. The color coding is the same as for panel (c). As can be seen, there are appreciable differences between the different molecular-frame components (both translational and rotational) as well as between the translational and rotational mode dynamics.
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Figure 2
(a) Instantaneous temperature evolution for flexible TIP3P water; the black curve shows the temperature for a system in equilibrium at 330 K (case 1); case 2 (blue line) is the temperature evolution for a system of the same size in which all the kinetic energy is initially put in translational modes, while in case 3 (red) the kinetic energy is initially concentrated in rotational modes only, and in case 4 (green) the kinetic energy is initially distributed in internal (vibrational) modes only. The lower inset shows the evolution of $|T - T_{e}|$ , where $T_{e}$ is the equilibrium temperature, and where the different relaxation times can be clearly observed in the range up to 50 ps; the upper inset shows the temperature evolution obtained in similar simulations for the case of ice with a total kinetic energy corresponding to an equilibrium temperature of 100 K (see Sec. 2). Panel (b) shows the decomposition of the kinetic energy into translational and rotation plus vibrational contributions for the four cases displayed in panel (a), with the same color coding. Panel (c) shows the evolution of the instantaneous temperature during the process of equilibration when the kinetic energy is initially distributed according to cases 1, 2, and 3 as in panel (a), during “heating” and “cooling” simulations (see the text).
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