Recent advances in quantum simulators permit unitary evolution interspersed with locally resolved midcircuit measurements. This paves the way for the observation of large-scale space-time structures in quantum trajectories and opens a window for the in situ analysis of complex dynamical processes. We demonstrate this idea using a paradigmatic dissipative spin model, which can be implemented, e.g., on Rydberg quantum simulators. Here, already the trajectories of individual experimental runs reveal surprisingly complex statistical phenomena. In particular, we exploit free-energy functionals for trajectory ensembles to identify dynamical features reminiscent of hydrophobic behavior observed near the liquid-vapor transition in the presence of solutes in water. We show that these phenomena are observable in experiments and discuss the impact of common imperfections, such as readout errors and disordered interactions.

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• Open quantum systems
• Quantum simulation
• Quantum many-body systems
• Stochastic dynamical systems
• Stochastic processes & statistics
• Tensor network methods