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foundations

Entropy

11 items

Entropy must be read through its declared channel, units, system boundary, and any represented exchange.

RelatedCoherenceOpen systemsReciprocitythermodynamicsFRC 566 seriesgaianarrativesphilosophy

Primary research (3)

PrimaryPaperv2.62026-07-12

Coherence in Chaos: Diffusion, Localization, and Decoherence in the Standard Map / Quantum Kicked Rotor Family

FRC 100.002 v2.6 preserves the Standard Map / Quantum Kicked Rotor chaos program, the KAM-structure functional, localization/decoherence pilots, the Ruelle-Pollicott negative result, and the demoted stadium appendix. It records the completed registered dense classical Gate 4 test as a negative result: fine KAM-area tracking fails, while the earlier coarse zero-parameter magnitude correspondence survives in its scoped form. This route does not promote the paper as a pillar. The canonical reciprocity law remains dS + k* d ln C = 0. In this paper's declared information-nat realization k*_{mu_nat}=1, and J_sys=d[S_sys,mu+k*_{mu_nat} ln C_mu]/dt remains a system-only diagnostic, not automatically entropy production or a boundary residual.

PrimaryPaperv2.22026-07-09

Entropy-Coherence Reciprocity and the Universal Coherence Condition v2.2

FRC 566.001 states entropy-coherence reciprocity in its canonical scale-invariant form dS + k* d ln C = 0. The starred Boltzmann bridge k* is not an ordinary tunable constant and is never fitted to an outcome or evolving state. Experiments and computations instantiate the same law at a declared register mu as dS_mu + k*_mu d ln C_mu = 0, with explicit entropy channel, coherence channel, units, and boundary. FRC uses the relation operationally as bookkeeping and proposes its open-system physical extension as a conjecture. Standard entropy production remains non-negative, but no toy closure is promoted into a universal directional replacement. The exact von Mises calculation and the Langevin boundary probe remain scoped results. The corrected information projection is retained: C[q]/C[p] depends on the entropy difference, not generally on D_KL(p||q), and C_XY = C_X C_Y exp(+I/k*).

PrimaryPaperv1.32026-07-09

Reciprocity in Action v1.3: Exact System-Only Motion and a Scoped Boundary Test

FRC 566.030 applies the canonical reciprocity law dS + k* d ln C = 0 through one explicit information-unit realization. With the predeclared representation k*_{mu_nat}=1, it computes Q=S+k*_{mu_nat} ln C exactly on the von Mises/Kuramoto family. Q is non-constant and reaches its unique stationary point at kappa r=1, kappa=1.608279 and C=0.621782. The exact identity is dS/d ln C=-kappa r, hence dQ/d ln C=k*_{mu_nat}-kappa r. This stationary point is dQ=0; it is not sigma_566=0 unless an explicit environment model supplies that additional equality. The family contains no bath and therefore measures neither irreversible production nor entropy export. A companion Langevin closure tests those quantities in one model class and finds no universal erasure floor in its declared normalization.

Concepts and topics (1)

Philosophical work (2)

Archive / development history (5)