As a liquid approaches the glass transition, its properties are dominated by local potential minima in its energy landscape. The liquid experiences localized vibrations in the basins of attraction surrounding the minima, and rearranges via relatively infrequent inter-basin jumps. As a result, the liquid dynamics at low temperature are related to the system's exploration of its own configuration space. The 'thermodynamic approach' to the glass transition considers the reduction in configuration space explored as the system cools, and predicts that the configurational entropy (a measure of the number of local potential energy minima sampled by the liquid) is related to the diffusion constant. Here we report a stringent test of the thermodynamic approach for liquid water (a convenient system to study because of an anomalous pressure dependence in the diffusion constant). We calculate the configurational entropy at points spanning a large region of the temperature-density plane, using a model that reproduces the dynamical anomalies of liquid water. We find that the thermodynamic approach can be used to understand the characteristic dynamic anomalies, and that the diffusive dynamics are governed by the configurational entropy. Our results indicate that the thermodynamic approach might be extended to predict the dynamical behaviour of supercooled liquids in general.

We report a numerical study, covering a wide range of packing fraction Phi and temperature T, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number n(max) of bonded interactions. We show that, when n(max)<6, the liquid-gas coexistence region shrinks, giving access to regions of low Phi where dynamics can be followed down to low T without an intervening phase separation. We characterize these arrested states at low densities (gel states) in terms of structure and dynamical slowing down, pointing out features which are very different from the standard glassy states observed at high Phi values.

We study thermodynamic and dynamic properties of a rigid model of the fragile glass-forming liquid orthoterphenyl. This model, introduced by Lewis and Wahnström in 1993, collapses each phenyl ring to a single interaction site; the intermolecular site-site interactions are described by the Lennard-Jones potential whose parameters have been selected to reproduce some bulk properties of the orthoterphenyl molecule. A system of N=343 molecules is considered in a wide range of densities and temperatures, reaching simulation times up to 1 micros. Such long trajectories allow us to equilibrate the system at temperatures below the mode coupling temperature T(c) at which the diffusion constant reaches values of order 10(-10) cm(2)/s and thereby to sample in a significant way the potential energy landscape in the entire temperature range. Working within the inherent structures thermodynamic formalism, we present results for the temperature and density dependence of the number, depth and shape of the basins of the potential energy surface. We evaluate the total entropy of the system by thermodynamic integration from the ideal-noninteracting-gas state and the vibrational entropy approximating the basin free energy with the free energy of 6N-3 harmonic oscillators. We evaluate the configurational part of the entropy as a difference between these two contributions. We study the connection between thermodynamical and dynamical properties of the system. We confirm that the temperature dependence of the configurational entropy and of the diffusion constant, as well as the inverse of the characteristic structural relaxation time, are strongly connected in supercooled states; we demonstrate that this connection is well represented by the Adam-Gibbs relation, stating a linear relation between logD and the quantity 1/TS(c). This relation is found to hold both above and below the critical temperature T(c)-as previously found in the case of silica-supporting the hypothesis that a connection exists between the number of basins and the connectivity properties of the potential energy surface.

Depth, number, and shape of the basins of the potential energy landscape are the key ingredients of the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only on the volume dependence of these landscape properties is derived. Vibrational and configurational contributions to pressure are sorted out in a transparent way. Predictions are successfully compared with data from extensive molecular dynamics simulations of a simple model for the fragile liquid orthoterphenyl.PACS numbers: 64.70. Pf, 61.20.Ja, 61.20.Lc Recent years have seen a resurgence in studies devoted to modeling the thermodynamics of supercooled liquids [1,2,3,4,5]. Such studies aim to elucidate the physics of the liquid-glass transition, to develop a thermodynamic description of out of equilibrium systems and to provide keys for a deeper understanding of the dynamics of supercooled states [6]. Numerical studies, boosted by increased computational resources which now allow simulations to track the slowing down of the dynamics over more than 6 decades in time, are providing quantitative estimates for the free energy of simple model systems [7,8,9,10]. The availability of such data provides stringent tests of the theoretical predictions [9,10,11] and helps in the understanding of basic mechanisms associated with the behavior of thermodynamic and dynamic quantities close to the glass transition.Among the thermodynamic formalisms amenable to numerical investigation, a central role is played by the Inherent Structure (IS) formalism introduced by Stillinger and Weber [12]. Properties of the potential energy landscape (PEL), such as depth, number and shape of the basins of the potential energy surface are calculated and used in the evaluation of the liquid free energy [9,10,11,13] In the IS formalism, the system free energy is expressed as a sum of an entropic contribution, accounting for the number of the available basins, and a vibrational contribution, expressing the free energy of the system when constrained in one of the basins [12].Important progress has been made after the discovery that -for models of fragile liquids -the number Ω(e IS ) of distinct basins of depth e IS in a system of N atoms or molecules is well described by a Gaussian distribution [10,14] Ω(e IS ) = e αN eHere the amplitude e αN accounts for the total number of basins. Numerical studies of models for fragile liquids have also shown that the basin free energy can be written as the depth e IS plus a vibrational contribution which, in the harmonic approximation, has the well known formwhere ω i (e IS ) is the i-th normal mode frequency (i = 1...M ) and β = 1/k B T . The M normal mode frequencies define the shape of the basin. If relevant, anharmonic corrections can also be accounted for [11,13]. The quantityln(ω i (e IS )/ω o ) (where ω o is the frequency unit) is found to depend linearly on the basin depth [10], i.e. can be written, in t...

Within the inherent structure (IS) thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)] we address the basic question of the physics of the liquid-liquid transition and of density maxima observed in some complex liquids such as water by identifying, for the first time, the statistical properties of the potential energy landscape (PEL) responsible for these anomalies. We also provide evidence of the connection between density anomalies and the liquid-liquid critical point. Within the simple (and physically transparent) model discussed, density anomalies do imply the existence of a liquid-liquid transition.PACS numbers: 64.70 Pf, 61.20.Ja, 64.20. Lc Water, the most important liquid for life, belongs to a class of liquids for which the isobaric temperature dependence of the density has a maximum. In contrast to ordinary liquids, water expands on cooling below 4C at atmospheric pressure. This density anomaly is associated with other thermodynamic anomalies, such as minima in the compressibility along isobars and an increase of the specific heat on cooling [1]. Recent fascinating studies have attempted to connect these anomalies to the presence of two different liquid structures, separated at low temperature by a line of first order transitions, ending in a second order critical point [2,3,4]. In the case of water, this novel critical point would be located in an experimentally inaccessible region [5]. Despite this unfavorable location, the postulated presence of this critical point provides a framework for interpreting [6] not only features of the liquid state but also the phenomenon of polyamorphism and the first-order like transition between polyamorphs [7]. In this Letter we aim at identifying the statistical properties of the potential energy landscape (PEL) responsible for the density maxima and the connection to the physics of the liquid-liquid transition.The study of the statistical properties of the PELi.e. of the number, shape and depth of the basins composing the potential energy hypersurface -is under tremendous development. Theoretical approaches, based on the seminal work of Stillinger and Weber [8], combined either with calorimetric data [9,10,11] or with analysis of extensive numerical simulations [12,13,14] are starting to provide precise estimates of the statistical properties of the PEL in several materials and models for liquids. A simple model for the statistical properties of the landscape, supported by recent numerical studies [14,15,16], can be built on the basis of the two following hypotheses:1. a gaussian distribution for Ω(e IS )de IS [15,17,18,19,20], the number of distinct basins of energy depth e IS between e IS and e IS + de IS , i.e.Here e αN counts the total number of PEL basins, (N being the number of molecules) E 0 is the characteristic energy scale and σ 2 is the variance of the distribution. A gaussian distribution is suggested by the central limit theorem, since in the absence of diverging correlation, e IS...