Maxwell’s Demon Unbound: Infinite Memory, the Second Law, and the Limits of Physical Agency

The standard information-theoretic exorcism of Maxwell’s demon holds that a demon must eventually erase its memory, and that by Landauer’s principle this erasure produces enough entropy to save the second law. Whatever its merits, this resolution rests entirely on an unexamined premise: that the demon is finite. This paper asks what follows when the premise is dropped. I argue, first, that a demon with unbounded memory evades the Landauer accounting entirely, and that the standard reply, on which the demon’s growing record itself serves as an entropy sink, succeeds only relative to a description that treats the record as unknown, which for the demon it is not. Second, drawing on the Gibbsian tradition of Jaynes and Myrvold, I argue that the unbounded demon does not so much violate the second law as expose its status: the law is a constraint on what agents with bounded means can do, not a bare fact about matter. Third, I show that the microscopic reversibility of dynamics gives the unbounded demon a startling further power, the recoverability in principle of any past configuration, and I make explicit the no-collapse assumption on which this depends. Fourth, I argue that such a being is nonetheless impossible within the physical universe, on two independent grounds: the Bekenstein bound, which caps the information content of any bounded region, and self-measurement theorems, which forbid any internal system from perfectly knowing a whole that includes itself. The unbounded demon is thus exiled to the boundary of physics, where, as Tipler’s Omega Point and the older tradition of divine memory suggest, the concept has always had another name. The second law, I conclude, is best understood as the signature of finitude: the price an agent pays for being a part of the world rather than the whole of it.