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|{{EquationRef|1}}}}

|{{EquationRef|1}}}}

Here <math>X_t^j</math> represents the microscopic variable at time t in the j-th dimension, and <math>V_t ; V_{t + 1}</math> respectively represent macroscopic state variables at two consecutive times. Rosas et al. defined that when <math>\mathrm{\Psi}>0</math>, emergence occurs in the system; but when <math>\mathrm{\Psi}<0</math>, we cannot determine whether the system has emergence, because this condition is only a sufficient condition for the occurrence of causal emergence.

Here <math>X_t^j</math> represents the microscopic variable at time t in the j-th dimension, and <math>V_t ; V_{t + 1}</math> respectively represent macroscopic variables at two consecutive times. Rosas et al. defined that when <math>\mathrm{\Psi}>0</math>, emergence occurs in the system; but when <math>\mathrm{\Psi}<0</math>, we cannot determine whether the system has emergence, because this condition is only a sufficient condition for the occurrence of causal emergence.

* Indicator for judging [[downward causation]]:

* Indicator for judging [[downward causation]]: