NVU dynamics. II. Comparing to four other dynamics

Perspective: Excess-entropy scaling

This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.

Isomorph theory of physical aging

This paper derives and discusses the configuration-space Langevin equation describing a physically aging R-simple system and the corresponding Smoluchowski equation. Externally controlled thermodynamic variables like temperature, density, and pressure enter the description via the single parameter T_s/T, in which T is the bath temperature and T_s is the "systemic" temperature defined at any time t as the thermodynamic equilibrium temperature of the state point with density ρ(t) and potential energy U(t). In equilibrium, T_s ≅ T with fluctuations that vanish in the thermodynamic limit. In contrast to Tool's fictive temperature and other effective temperatures in glass science, the systemic temperature is defined for any configuration with a well-defined density, even if it is not close to equilibrium. Density and systemic temperature define an aging phase diagram, in which the aging system traces out a curve. Predictions are discussed for aging following various density-temperature and pressure-temperature jumps from one equilibrium state to another, as well as for a few other scenarios. The proposed theory implies that R-simple glass-forming liquids are characterized by the dynamic Prigogine-Defay ratio being equal to unity.

Simple liquids' quasiuniversality and the hard-sphere paradigm

This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.

Computer simulations of glasses: the potential energy landscape

We review the current state of research on glasses, discussing the theoretical background and computational models employed to describe them. This article focuses on the use of the potential energy landscape (PEL) paradigm to account for the phenomenology of glassy systems, and the way in which it can be applied in simulations and the interpretation of their results. This article provides a broad overview of the rich phenomenology of glasses, followed by a summary of the theoretical frameworks developed to describe this phenomonology. We discuss the background of the PEL in detail, the onerous task of how to generate computer models of glasses, various methods of analysing numerical simulations, and the literature on the most commonly used model systems. Finally, we tackle the problem of how to distinguish a good glass former from a good crystal former from an analysis of the PEL. In summarising the state of the potential energy landscape picture, we develop the foundations for new theoretical methods that allow the ab initio prediction of the glass-forming ability of new materials by analysis of the PEL.

Effect of Size Polydispersity on the Nature of Lennard-Jones Liquids

Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. We study here the effect of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to size polydisperse fluids and can be used to improve even further the understanding of these intriguing systems.

Simplicity of condensed matter at its core: generic definition of a Roskilde-simple system

The isomorph theory is reformulated by defining Roskilde-simple systems by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a different density. If the potential energy as a function of all particle coordinates is denoted by U(R), this requirement translates into U(Ra) < U(Rb) ⇒ U(λRa) < U(λRb). Isomorphs remain curves in the thermodynamic phase diagram along which structure, dynamics, and excess entropy are invariant, implying that the phase diagram is effectively one-dimensional with respect to many reduced-unit properties. In contrast to the original formulation of the isomorph theory, however, the density-scaling exponent is not exclusively a function of density and the isochoric heat capacity is not an exact isomorph invariant. A prediction is given for the latter quantity's variation along the isomorphs. Molecular dynamics simulations of the Lennard-Jones and Lennard-Jones Gaussian systems validate the new approach.

Isomorphs, hidden scale invariance, and quasiuniversality

This paper first establishes an approximate scaling property of the potential-energy function of a classical liquid with good isomorphs (a Roskilde-simple liquid). This "pseudohomogeneous" property makes explicit that-and in which sense-such a system has a hidden scale invariance. The second part of the paper gives a potential-energy formulation of the quasiuniversality of monatomic Roskilde-simple liquids, which was recently rationalized in terms of the existence of a quasiuniversal single-parameter family of reduced-coordinate constant-potential-energy hypersurfaces [J. C. Dyre, Phys. Rev. E 87, 022106 (2013)]. The new formulation involves a quasiuniversal reduced-coordinate potential-energy function. A few consequences of this are discussed.

NVU dynamics. III. Simulating molecules at constant potential energy

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, J. Chem. Phys. 135, 104101 (2011); T. S. Ingebrigtsen, S. Toxvaerd, T. B. Schrøder, and J. C. Dyre, ibid. 135, 104102 (2011)], a numerical algorithm for simulating geodesic motion of atomic systems was developed and tested against standard algorithms. The conclusion was that the NVU algorithm has the same desirable properties as the Verlet algorithm for Newtonian NVE dynamics, i.e., it is time-reversible and symplectic. Additionally, it was concluded that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit. In this paper, the NVU algorithm for atomic systems is extended to be able to simulate the geodesic motion of molecules at constant potential energy. We derive an algorithm for simulating rigid bonds and test this algorithm on three different systems: an asymmetric dumbbell model, Lewis-Wahnström o-terphenyl (OTP) and rigid SPC/E water. The rigid bonds introduce additional constraints beyond that of constant potential energy for atomic systems. The rigid-bond NVU algorithm conserves potential energy, bond lengths, and step length for indefinitely long runs. The quantities probed in simulations give results identical to those of Nosé-Hoover NVT dynamics. Since Nosé-Hoover NVT dynamics is known to give results equivalent to those of NVE dynamics, the latter results show that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit also for molecular systems.

NVU perspective on simple liquids' quasiuniversality

The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.