The Negative-Entropy Construction: A Structural Dynamics Framework for Civilization

We propose the Negative-Entropy Construction, a structural dynamics framework that models civilization as a localized negative-entropy system constrained by reflex arcs, relational carrying capacity, and cyclic regeneration. Moving beyond rational-optimization assumptions, we treat civilization as an open, dissipative structure whose behavior is driven by pressure to maintain structural continuity while accommodating energy flows.

The framework is organized around a two-layer construction. The first layer provides a phenomenological formal slice: the synergy between rationality H and instinct G, stabilized entropy P, governance cost S, free energy F, stability pressure \Pi, and emotional impulse \Phi. The second layer is a network dynamical realization on a directed, weighted reflex-arc network, governed by node variables (A_i,B_i,I_i) and edge weights w_{ij}=w^T_{ij}+w^R_{ij}. No one-to-one identification between the phenomenological variables and network coordinates is assumed.

A central clarification concerns the interface variable I. It is not a conserved inventory requiring restoration to a target value I^\ast. It is the non-equilibrium interface generated by the relation A\leftrightarrow B. The reference level I^\ast is a reference interface level associated with the symmetric configuration; it is not an attractor.

The system decomposes into four structurally distinct sectors:

· the local balancing mode A-B, strictly damped;

· the envelope sector q=0, drifting and coupled to the uniform edge mode;

· the circulation sector q=1,2, possibly exhibiting a Hopf bifurcation at threshold \lambda_H;

· the slow capacity variable C_I\equiv\Xi_{\max}, the realizability envelope.

The framework involves two distinct time scales. On the fast scale, Hopf circulation produces instantaneous dissipation. On the slow scale T=\varepsilon t, secular carrying drift occurs, driven by parameter evolution. A crucial mathematical clarification: on an exact Hopf limit cycle at fixed parameters, \langle\dot E_B\rangle_T=0 holds identically for any state function of a periodic orbit. No spontaneous period-averaged carrying depletion exists.

We establish the following chain as model-internal results:

\lambda>\lambda_H

\;\Rightarrow\;

r_\ast^2>0

\;\Rightarrow\;

\langle D_I\rangle=Q_Jr_\ast^2>0

\;\Rightarrow\;

\kappa_B^{(D)}<0

where \kappa_B^{(D)}=-\frac{\mu_I}{4}\sum_iR_i^\ast|(L_Jq_H)_i|^2 is strictly negative. The total sensitivity \kappa_B depends on node, transport, flux, and edge-degradation contributions. The slow carrying drift is driven by parameter evolution:

\frac{d\lambda}{dT}

\;\Rightarrow\;

\frac{dr_\ast^2}{d\lambda}

\;\Rightarrow\;

\kappa_B

\;\Rightarrow\;

\frac{d\bar E_B}{dT}

\;\Rightarrow\;

\frac{d\Xi_{\max}}{dT}

\;\Rightarrow\;

\frac{dM}{dT}

The death condition is

\left|\frac{d\bar E_B}{dT}\right|>R_B

where R_B is the regeneration rate of instinctive carrying capacity. Completion of the chain to envelope failure requires explicit Closure Conditions, stated in Section 10.

No numerical predictions, empirical calibration, or historical judgments are offered.