Spontaneous energy-barrier formation in entropy-driven glassy dynamics

The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough potential energy landscape and we analyze it both numerically and analytically. The model provides an example of dynamics where typical relaxation channels go over finite-potential energy barriers despite the presence of less-energy-demanding escaping paths in configurational space; we expect this phenomenon to be also relevant in the thermally activated regime of realistic models of glass-formers. In this case, we found that typical dynamical paths episodically reach an high-fixed-threshold energy, unexpectedly giving rise to a simple thermally activated aging phenomenology. In order to unveil this peculiar aging behavior, we introduce a novel description of the dynamics in terms of spontaneously emerging dynamical basins.