. 2018 Mar 5;20(3):169. doi: 10.3390/e20030169

Table 3.

Deterministic components of the PID terms for the trivariate decomposition derived from the weak stochasticity axiom. All terms not included in the table have no deterministic component due to the axiom. These expressions correspond to the case in which the primary source i overlaps with the target. If i does not overlap, $Δ_{d} (X; i)$ and $Δ_{d} (X; i . j k)$ are zero, while the other terms depend on their characteristic symmetry for the other variables j and k, and vanish if none of the variables with the corresponding symmetry overlaps with the target. See the main text and Appendix E for details.

Term	Measure
$Δ_{d} (X; i)$	$H (i \| j k, X - i j k)$
$Δ_{d} (X; i . j k)$	$I (X - j k; j k \ j, k) - I (X - i j k; j k \ j, k)$
$Δ_{d} (X; i . j)$	$I (i; j \| k, X - i j k) - [Δ_{d} (X; i . j k) + Δ_{d} (X; j . i k)]$
$Δ_{d} (X; i . j . k)$	$C (i; j; k \| X - i j k) + Δ_{d} (X; i . j k) + Δ_{d} (X; j . i k) + Δ_{d} (X; k . i j)$