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In principle, all of the dynamical complexities of many-body systems areencapsulated in the potential energy landscapes on which the atoms move - anobservation that suggests that the essentials of the dynamics ought to bedetermined by the geometry of those landscapes. But what are the principalgeometric features that control the long-time dynamics? We suggest that the keylies not in the local minima and saddles of the landscape, but in a more globalproperty of the surface: its accessible pathways. In order to make this notionmore precise we introduce two ideas: (1) a switch to a new ensemble thatremoves the concept of potential barriers from the problem, and (2) a way offinding optimum pathways within this new ensemble. The potential energylandscape ensemble, which we describe in the current paper, regards the maximumaccessible potential energy, rather than the temperature, as a controlvariable. We show here that while this approach is thermodynamically equivalentto the canonical ensemble, it not only sidesteps the idea of barriers, itallows us to be quantitative about the connectivity of a landscape. Weillustrate these ideas with calculations on a simple atomic liquid and on theKob-Andersen model of a glass-forming liquid, showing, in the process, that thelandscape of the Kob-Anderson model appears to have a connectivity transitionat the landscape energy associated with its mode-coupling transition. We turnto the problem of finding the most efficient pathways through potential energylandscapes in our companion paper.

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