Solvation in Space-Time: Pre-Transition Effects in Trajectory Space

We demonstrate pre-transition effects in space-time in trajectories of systems in which the dynamics displays a first-order phase transition between distinct dynamical phases. These effects are analogous to those observed for thermodynamic first-order phase transitions, most notably the hydrophobic effect in water. Considering the East model as an example, we study the properties of space-time 'solvation' by examining trajectories where finite space-time regions are conditioned to be inactive in an otherwise active phase. We find that solvating an inactive region of space-time within an active trajectory shows two regimes in the dynamical equivalent of solvation free energy: an 'entropic' small solute regime in which uncorrelated fluctuations are sufficient to evacuate activity from the solute, and an 'energetic' large solute regime that involves formation of a solute-induced inactive domain with an associated active--inactive interface bearing a dynamical interfacial tension. As a result of this dynamical tension there is a dynamical analog of the hydrophobic collapse that drives the assembly of large hydrophobes in water. We discuss the general relevance of these results to properties of dynamical fluctuations in systems with slow collective relaxation such as glass formers.