How to quantify change after restricting an agent's actions?

I am studying independent agents acting in a discrete environment. At state $s$ , an agent has an admissible action set $A(s)$ . A constraint $C$ does not directly prescribe a new probability distribution. Instead, it deterministically modifies the available action set: $$A(s) \longrightarrow A_C(s) \subseteq A(s).$$ For example, if $$A(s)=\{a_1,a_2,a_3\},$$ a constraint may make $a_1$ unavailable while leaving $a_2$ and $a_3$ available: $$A_C(s)=\{a_2,a_3\}.$$ Independent fresh agent sessions are then exposed to the same condition. I do not define $P_C$ by renormalizing the original distribution $P$ . Rather, $P_C$ is the empirical distribution of the choices produced by the agents under $A_C(s)$ . Thus the mechanism is: $$C \longrightarrow A_C(s) \longrightarrow \text{agent choices} \longrightarrow P_C.$$ After the constraint is removed, the original action set becomes available again: $$A_C(s) \longrightarrow A(s),$$ and I can similarly estimate a post-constraint empirical distribution $P_{\mathrm{post}}$ . My statistical question is: What is an appropriate information-theoretic way to distinguish the trivial reduction of possibilities caused directly by $A_C(s)\subseteq A(s)$ from a genuine change in the agents' probability distribution over the actions that remain available? In particular, I would like a quantity or decomposition that does not interpret a mechanical reduction of the action space itself as increased "organization," but can detect redistribution of probab…