Jocelyne Muller

This paper does not claim to refute the second law of thermodynamics. It argues that a long-standing question — whether the totality is entropic — is malformed, and locates the malformation in the terms it employs. Entropy, in every standard formulation, is defined relative to a partition: a coarse-graining of states into macrostates, or a division of a whole into subsystems. The totality — defined here as a structure for which no larger containing structure exists — admits no such partition from without, and a pure global state, taken whole, carries zero entropy by the standard quantum measure; nonzero entropy appears only upon partition. A quantity defined by partition therefore has no determinate value for a whole that cannot be partitioned from without; the apparent value zero is the reference origin, not a measured magnitude, and to read it as a magnitude is to assume a privileged absolute frame of the kind relativity abolished. Beneath this lies a more general condition: our way of knowing proceeds sequentially, one confirmed step after another, by isolating one thing at a time — which is to say, by partition — while the totality is non-linearly coupled, every part interfering with every other, isolable nowhere. A sequential method cannot grasp a non-linear whole. The argument is, by open declaration, as much an exercise in semantics, in the rigorous sense, as in physics or metaphysics, and it keeps three registers — linguistic, mathematical, physical — explicitly apart. It distinguishes what is claimed (a scope clarification) from what is not (a physical result), engages the relevant literature, and names the formal problems whose resolution would carry the question further. It is offered as a provocation, in the frank expectation that a better and more comprehensive way of putting the question exists, which we do not yet possess.