First published: January 13, 2025
Last revised: January 21, 2025

Let's define a state space for consciousness where the states are the collection of qualia experienced by a conscious being. This state space is large but finite, because when qualia are too similar they become indistinguishale, so there is a minimum state space volume and a topology.

I think one of two options has to be true: either the state space of consciousness somehow tracks the state space of the physical constitutents of the brain (its molecules, cells and so on), or it adds to it. And I think there may be a thermodynamic argument for testing this second hypothesis.

You can always assign a probability distribution over the state space of a system, which depends on what you know about it. The max entropy principle helps with this assignment. To reduce the entropy of the probability distribution you need to either measure the system and extract information or act on the system and change its state, for instance to ensure that it will always end up in the same state space volume (which is a non-reversible transformation). To do the latter you need to pay a price in terms of some conserved quantity like energy or momentum, etc. Also, the entropy that you extract needs to end up somewhere. This is essentially Landauer's principle.

Maxwell's demon can lower the entropy of a probability distribution over the states of a system "for free" because the probability distribution that he assigns has a much lower entropy than the probability we can assign by only knowing macroscopic properties. This is obviously cheating, in fact the demon cannot lower the entropy of the system below that of his own distribution.

So here's the idea: by definition a being experiencing their consciousness has exact knowledge of its state, and so from their perspective they are like Maxwell's demon of their own consciousness. So can we distinguish zombies from conscious beings via some thermodynamic signature?