Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: the potential energy landscape ensemble.

In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move--an observation that suggests that the essentials of the dynamics ought to be determined by the geometry of those landscapes. But what are the principal geometric features that control the long-time dynamics? We suggest that the key lies not in the local minima and saddles of the landscape, but in a more global property of the surface: its accessible pathways. In order to make this notion more precise we introduce two ideas: (1) a switch to a new ensemble that deemphasizes the concept of potential barriers, and (2) a way of finding optimum pathways within this new ensemble. The potential energy landscape ensemble, which we describe in the current paper, regards the maximum accessible potential energy, rather than the temperature, as a control variable. We show here that while this approach is thermodynamically equivalent to the canonical ensemble, it not only sidesteps the idea of barriers it allows us to be quantitative about the connectivity of a landscape. We illustrate these ideas with calculations on a simple atomic liquid and on the Kob-Andersen [Phys. Rev. E 51, 4626 (1995)] of a glass-forming liquid, showing, in the process, that the landscape of the Kob-Anderson model appears to have a connectivity transition at the landscape energy associated with its empirical mode-coupling transition. We turn to the problem of finding the most efficient pathways through potential energy landscapes in our companion paper.