IndisputableMonolith.Physics.MaxwellDemon_FromJCost
Formalizes Maxwell's demon as a recognition-cost obstruction: any attempt to sort microstates without paying the J-cost hits a strictly positive canonical threshold. Physicists citing RS thermodynamics or Landauer-type bounds use this module. The development is mostly definitions plus nonnegativity and positivity lemmas, capped by an inhabited certificate structure.
claimA domain cost $C$ built from the recognition cost $J$ is nonnegative, and there is a canonical threshold $\theta>0$ such that any Maxwell-demon sorting operation that would reduce disorder without external work must pay at least $\theta$. The module packages this as a certificate record asserting the obstruction.
background
Recognition Science measures mismatch by the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced uniquely by the Recognition Composition Law. In RS-native units the fundamental tick is $\tau_0=1$. The Cost import supplies the analytic properties of $J$ used here.
Maxwell's demon is the classical thought experiment in which a gatekeeper sorts hot and cold molecules and appears to lower entropy without work. In this module the "work" is recognition cost on the configuration ratio: a domain cost functional is defined so that equality cases and nonnegativity are immediate from $J$, and a canonical positive threshold marks the minimal cost of a successful sort.
The local setting is pure physics scaffolding inside IndisputableMonolith: no continuum statistical mechanics, only the discrete J-ladder cost that already underlies mass and coupling derivations elsewhere in the monolith.
proof idea
Definition-heavy module. domainCost is introduced from J; domainCost_at_eq and domainCost_nonneg are short algebraic consequences of J's minimum at 1 and J>=0. canonicalThreshold is a positive constant (canonicalThreshold_pos). MaxwellDemonCert is a structure bundling the cost obstruction; cert and cert_inhabited supply a concrete inhabited instance. No deep tactic proof: the argument is "J-cost is nonnegative and vanishes only at balance, hence any demon gate that creates imbalance pays a fixed positive floor."
why it matters in Recognition Science
Places Maxwell's demon inside the same J-cost ledger that forces T5 (J-uniqueness) and the RS constants, rather than as a separate information-theoretic parable. Downstream graph is currently empty, so this module is a leaf certificate: it records that the demon cannot operate below the canonical threshold once recognition cost is the only allowed ledger. It aligns with Landauer-style "information is physical" claims, but the currency is J, not kT ln 2. Useful as a physics-facing sanity check that the cost functional used for masses and alpha also blocks free sorting.
scope and limits
- Does not derive continuum entropy production or Clausius inequality from J.
- Does not model a concrete molecular gate or Szilard engine dynamics.
- Does not prove thermodynamic second law in full statistical mechanics.
- Does not connect the threshold numerically to kT ln 2 or Landauer's limit.
- Does not feed a named parent theorem yet (no used_by edges).