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When the governing equations of a deterministic nonlinear system are integrated with respect to time from the most probable state at an initial time, the predicted state is not necessarily the most probable state.If the trace of the Jacobian matrix of the governing equations does not depend on the state variables (hereafter referred to as the trace condition) and the initial probability density function (PDF) is unimodal, the predicted PDF remains unimodal and the mode of PDF evolves according to the governing equations.