It is possible to formulate the thermodynamics of a glass forming system in terms of the properties of inherent structures, which correspond to the minima of the potential energy and build up the potential energy landscape in the high-dimensional configuration space. In this work we quantitatively apply this general approach to a simulated model glass-forming system. We systematically vary the system size between N=20 and N=160. This analysis enables us to determine for which temperature range the properties of the glass former are governed by the regions of the configuration space, close to the inherent structures. Furthermore, we obtain detailed information about the nature of anharmonic contributions. Moreover, we can explain the presence of finite size effects in terms of specific properties of the energy landscape. Finally, determination of the total number of inherent structures for very small systems enables us to estimate the Kauzmann temperature.

Computer simulations of a model glass-forming system are presented, which are particularly sensitive to the correlation between the dynamics and the topography of the potential energy landscape. This analysis clearly reveals that in the supercooled regime the dynamics is strongly influenced by the presence of deep valleys in the energy landscape, corresponding to long-lived metastable amorphous states. We explicitly relate non-exponential relaxation effects and dynamic heterogeneities to these metastable states and thus to the specific topography of the energy landscape.It has been proposed a long time ago that a deeper understanding of relaxation processes in complex systems can be achieved by analysing the properties of the potential energy landscape in the high-dimensional configuration space. At sufficiently low temperatures the properties of the system are mainly dominated by the local energy minima (inherent structures) and the dynamics can be viewed as hopping processes between adjacent inherent structures [1]. Important information like the accessibility of the ground state in proteins [2,3] and clusters [4] or the relevance of substates in proteins [5] could indeed be gained by this approach. Although this approach has been also discussed for supercooled liquids [6,7], quantitative information is rare which might help to elucidate the specific properties like non-Arrhenius temperature behavior or non-exponential relaxation [8,9]. For example, no concrete evidence exists for the relevance of a few specific states in the dynamics of supercooled liquids in analogy to the substates of proteins.For approaching this problem via computer simulations, an appropriate diagnostic tool is to perform molecular dynamics (MD) simulations and to regularly quench the system, thus mapping the MD trajectory on a set of inherent structures [10]. Along this line Sastry et al. analysed a binary Lennard-Jones system upon cooling [11]. They observed that at nearly the same temperature T r the structural (α) relaxation becomes non-exponential and the average energy of the inherent structures starts to decrease. From the presence of a common onset temperature T r they concluded that for T < T r the dynamics is already influenced by the energy landscape [11]. However, only for even lower temperatures around the cricital temperature of the mode coupling theory [12] the dynamics can indeed be viewed as hopping between different inherent structures [13].In this Letter we combine the above method, yielding information about the inherent structures in configuration space, with a simultaneous determination of the mobility as a measure for the dynamics in real space. Thus we have a unique way of correlating the topography of the energy landscape with the dynamics in real space. This approach is, of 1

The thermodynamics of glass forming systems can be expressed via the density of inherent structures, which correspond to the minima of the potential energy landscape. In previous work this approach has been applied to Lennard-Jones type systems, yielding a density of inherent structures which to a very good approximation turned out to be gaussian. In this work we clarify whether the gaussian distribution is just a consequence of the central limiting theorem or whether it also contains information about the local structure of the glass-forming system.

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SUMMARY: In the rotational isomeric state (RIS) approach the conformational statistics of a polymer chain can be conveniently described in terms of the statistical matrix. In this work it is shown from a conceptual point of view to which degree the projection onto a few states, inherently present in any RIS approach, may lead to systematic deviations for estimation of the a priori probabilities. It is shown that these deviations scale with some power of the inverse temperature. Furthermore an algorithm is presented, deriving the statistical matrix from computer simulations. This algorithm is applied to polyethylene. Comparison with the conformational statistics as obtained from Monte Carlo simulations allows the quality of the statistical matrix elements to be estimated. It turns out that the systematic deviation does not hamper practical applications. Questions like the relevance of the anharmonicity of the energy landscape or consideration of more than nearest-neighbor correlations in the RIS approach are discussed.