IndisputableMonolith.Physics.LandauerPrincipleFromJCost
Packages Landauer's bound as a consequence of the Recognition Science J-cost: a domain cost, a positive canonical erasure threshold, and an inhabited certificate that irreversible bit erasure costs at least that threshold in RS-native units. Thermodynamics and information-physics workers connecting kT ln 2 to the forcing chain would cite it. The module is mostly definitional packaging with nonnegativity and positivity lemmas.
claimFrom the J-cost one defines a domain cost $C\ge 0$, a canonical Landauer threshold $\theta>0$, and a certificate asserting that irreversible erasure of one bit incurs cost at least $\theta$ in RS-native units (with $\tau_0=1$ tick).
background
Landauer's principle states that erasing one bit of information has a minimum thermodynamic cost proportional to $kT\ln 2$. Recognition Science derives costs from the unique J-functional forced at T5, $J(x)=(x+x^{-1})/2-1$, rather than from a separate thermodynamic postulate.
This module sits in the physics layer and imports the RS constants (including the fundamental tick $\tau_0=1$) and the Cost API. It treats irreversible domain change as the carrier of Landauer cost: the cost of a transition is read off J, and a canonical positive threshold is isolated as the one-bit erasure floor.
Sibling objects name that story directly: a domain cost with an evaluation lemma and a nonnegativity proof, a positive canonical threshold, and a LandauerCert bundle with an inhabited instance so downstream code can assume the bound holds.
proof idea
Definition module with light lemmas, not a deep derivation. It introduces domainCost from the imported J-cost, records evaluation and nonnegativity, defines canonicalThreshold and proves it is positive, then packages the Landauer claim as a certificate structure with a canonical inhabited witness. No multi-step tactic proof of the physical bound itself; the work is naming, positivity, and cert assembly on top of Cost and Constants.
why it matters in Recognition Science
Gives the physics layer a named Landauer object tied to J-cost uniqueness (forcing step T5) instead of an external thermodynamic axiom. That keeps irreversible information cost inside the same cost calculus used for the Recognition Composition Law and the phi-ladder mass formula. Downstream used-by edges are empty in the graph snapshot, so the module currently stands as a self-contained cert surface: other physics developments can require LandauerCert rather than re-deriving the threshold. It does not yet close a paper-level forcing theorem; it freezes the Landauer reading of J so later energy-accounting results have a stable handle.
scope and limits
- Does not derive kT ln 2 from statistical mechanics; works in RS-native cost units.
- Does not prove a full thermodynamic second law; only packages a one-bit erasure threshold.
- Does not connect the threshold to measured joules without a separate unit bridge.
- Does not supply used-by consumers in the current graph; it is a cert surface.
- Does not re-prove J-uniqueness; assumes the Cost API and T5 background.