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<math>f</math> is the state transition matrix of a Markov chain, [math]U(\mathcal{X})[/math] represents the uniform distribution over the value space [math]\mathcal{X}[/math] of the state variable [math]X_{t}{/math]. <math>\tilde{X}t,\tilde{X}{t+1}</math> are the states at two consecutive moments following the [[intervention]] of [math]X_{t}[/math] at time <math>t</math> into a [[uniform distribution]]. <math>p_{ij}</math> denots the transition probability from state <math>i</math> to state <math>j</math>. The formula shows that <math> EI </math> depends solely on the probability transition matrix [math]f[/math]. The intervention operation is ensures that effective information measures the causal effects of the dynamics objectively. This approach avoids influence from the original data distribution.  

<math>f</math> is the state transition matrix of a Markov chain, [math]U(\mathcal{X})[/math] represents the uniform distribution over the value space [math]\mathcal{X}[/math] of the state variable [math]X_{t}[/math]. [math]X_{t}[/math], [math]X_{t+1}[/math] are the states at two consecutive moments following the [[intervention]] of [math]X_{t}[/math] at time <math>t</math> into a [[uniform distribution]]. <math>p_{ij}</math> denots the transition probability from state <math>i</math> to state <math>j</math>. The formula shows that <math> EI </math> depends solely on the probability transition matrix [math]f[/math]. The intervention operation is ensures that effective information measures the causal effects of the dynamics objectively. This approach avoids influence from the original data distribution.