What question did this study set out to answer?

This research aims to model how consensus propagates in digital discourse through a novel theoretical framework.

June 17, 2026Open Access

Non-Linear Epistemic Field Theory & Social Hydrodynamics: A Macroscopic Continuum Model of Consensus Propagation and Narrative Solitons

Key Points

This research aims to model how consensus propagates in digital discourse through a novel theoretical framework.
Developed a non-linear epistemic field theory using a modified macroscopic wave equation.
Executed a Madelung transformation on a nonlinear Schrödinger equation to form a social fluid model.
Validated the model using a pseudo-spectral simulation engine to enforce real-time dynamic checks.
Identified narrative solitons as localized bound states within the social fluid model.
Revealed that collapsing the mean-field approximation leads to chaotic agent dynamics at the narrative level.
Demonstrated the emergence of ideological echo chambers in the context of networked discourse.

Abstract

Abstract: We develop a non-linear epistemic field theory mapping macro-scale consensus propagation over networked modern digital discourse via a modified, non-linear macroscopic wave equation. By executing a Madelung hydrodynamic transformation on a Nonlinear Schrödinger Equation (NLSE) coupled to an evolving information-substrate, we derive a self-focusing macroscopic social fluid model. Ideological echo chambers emerge natively as localized, non-dispersive bound states (`Narrative Solitons'). The network substrate features stigmergic wayfinding modeled through a variable kinetic mass operator matching the BenDaniel-Duke semiconductor formulation. Microscopic cognitive order-effects are handled via a Hilbert-Schmidt norm commutator architecture, scaled to classical pressure fields by population susceptibility factors. We expose an underlying socio-psychological paradox: driving memory relaxation to infinity collapses the mean-field approximation, transitioning continuous narratives into uncoupled chaotic discrete agent dynamics via a spatial decoherence phase transition. The model is validated via a stable, pseudo-spectral simulation engine enforcing an explicit, real-time dynamic Courant-Friedrichs-Lewy (CFL) limit check. Keywords: Non-Linear Epistemic Field Theory, Social Hydrodynamics, Narrative Solitons, Nonlinear Schrödinger Equation, Madelung Transformation, BenDaniel-Duke Operator, Algorithmic Stigmergy, Echo Chambers, Digital Discourse, Quantum Decision Theory, Cognitive Order-Effects, Spatial Decoherence, Phase Transition, Pseudo-Spectral Simulation, Computational Social Science, Epistemic Dynamics

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