I've been thinking about the classic Cartesian interaction problem lately, and it always bothered me that people treat it as just a metaphysical debate. When you try to frame it using even basic concepts from thermodynamics or state-space mechanics, the whole idea of "non-physical mind affecting physical matter" seems to fall apart immediately.
For one, if mental states (M) and physical states (P) are strictly disjoint sets (M ∩ P = Ø), any function mapping M onto P requires some kind of mediating channel. But if that channel interacts with physical matter, it has to have physical degrees of freedom. So the second you introduce a bridge to link them, that bridge is just physical. You can't really have a non-physical cause acting on matter without it taking on physical properties.
Landauer’s principle makes this even harder to ignore. Changing a physical state or erasing information takes actual physical work (at least kT ln 2 per bit). If a non-physical mind has zero physical energy to give, where is that energy coming from? You can't just alter physical bits for free without violating conservation of energy.
Also, if you look at it through state-space terms, two independent systems are a separable tensor product (Ψ = ψM ⊗ ψP). The moment you add an interaction operator between them, the state becomes entangled and non-separable (Ψ ≠ ψM ⊗ ψP). So the very act of interacting actually destroys the ontological independence dualists are trying to claim.
Am I oversimplifying this, or do modern dualists (like Chalmers or property dualists) just bite the bullet and reject physical closure altogether? Curious if there's any serious attempt to reconcile dualism with Landauer's principle or if it just gets brushed aside.