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Operationally, the ensemble average is described by starting an ensemble of trajectories, assuming the ensemble has a density, evolving it for a long time, and averaging the observable $J$ across the ensemble.

Conditions: One considers an ensemble of trajectories rather than a single trajectory.; The ensemble is assumed to have a density.; The average of $J$ is taken over the ensemble after long-time evolution.

Operationally, the ensemble average is described by starting an ensemble of trajectories, assuming the ensemble has a density, evolving it for a long time, and averaging the observable $J$ across the ensemble.

Conditions: One considers an ensemble of trajectories rather than a single trajectory.; The ensemble is assumed to have a density.; The average of $J$ is taken over the ensemble after long-time evolution.