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Emergent Discrete Interaction Events in a Variational Dissipative Conservative Framework

Kevin Ellis-Anderson

Published Dec 19, 2025• 1 citation
Publisher

Abstract

This preprint investigates the emergence of discrete interaction events within a variational dissipative–conservative partial differential equation framework introduced in earlier work. The fundamental dynamics consist of a unitary oscillatory field coupled to an irreversible dissipative auxiliary field, both generated by a single free-energy functional. While propagation remains continuous and wave-like, irreversible energy transfer to the dissipative sector induces localisation and produces discrete, event-like outcomes. No wavefunction collapse, stochastic dynamics, or particle ontology is introduced. Discreteness arises as an emergent consequence of variational irreversibility and monotonic free-energy decay. This work forms the third step in a sequence of papers developing the dynamical framework, effective decoherence, and event formation within the same variational setting.

DOI
10.5281/zenodo.17985639

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This preprint investigates the emergence of discrete interaction events within a variational dissipative–conservative partial differential equation framework introduced in earlier work. The fundamental dynamics consist of a unitary oscillatory field coupled to an irreversible dissipative auxiliary field, both generated by a single free-energy functional. While propagation remains continuous and wave-like, irreversible energy transfer to the dissipative sector induces localisation and produces discrete, event-like outcomes. No wavefunction collapse, stochastic dynamics, or particle ontology is introduced. Discreteness arises as an emergent consequence of variational irreversibility and monotonic free-energy decay. This work forms the third step in a sequence of papers developing the dynamical framework, effective decoherence, and event formation within the same variational setting.
This preprint develops a reduced dynamical description derived from a previously introduced variational dissipative–conservative PDE framework. Starting from a coupled system consisting of a unitary oscillatory field and a dissipative auxiliary field generated by a single free-energy functional, we show how effective decoherence arises when the auxiliary degrees of freedom are coarse-grained. The full system preserves unitary Hamiltonian evolution in the oscillatory sector, while non-unitary behaviour appears only at the reduced level through irreversible coupling. No collapse postulate, stochastic terms, or modification of quantum mechanics is introduced. The work focuses exclusively on decoherence and effective localisation as emergent phenomena within the variational framework and is intended as a companion to the foundational PDE formulation.
This paper presents a regime-based account of discrete event formation within a variational dissipative–conservative framework in which irreversibility and constraint are primary. Discrete interaction events are shown to arise when multiple jointly persistent oscillatory continuations become dynamically incompatible under accumulating irreversible constraint. Event formation is not treated as a stochastic collapse mechanism, observer-dependent process, or additional postulate, but as the deterministic failure of coexistence once compatibility thresholds are exceeded. The work does not modify quantum mechanics, introduce hidden variables, or propose new dynamical laws. Its contribution is explanatory and foundational, providing the structural link between entanglement, decoherence, and the emergence of classical behaviour.
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This deposit contains the paper “Emergence of a Quantum-Analogue Regime from Variational Dissipative–Conservative Dynamics” by Kevin Ellis Anderson. The paper analyses a regime of a previously introduced variational dissipative–conservative partial differential equation framework in which the conservative oscillatory sector admits an effective quantum-like description. Starting from deterministic Hamiltonian evolution coupled to auxiliary dissipative degrees of freedom, the work shows that an amplitude–phase decomposition of the oscillatory field yields a Schrödinger-type equation with an emergent effective Planck constant. The resulting dynamics are formally equivalent to quantum mechanics within a specific regime of validity, while remaining embedded in a broader variational system that also supports decoherent and classical limits. No modification of unitary evolution is introduced, and no stochastic elements, collapse postulates, or hidden variables are assumed. The paper does not propose a revision of quantum theory. Rather, it situates quantum behaviour as a regime arising from deterministic variational dynamics, with effective parameters determined by the underlying free-energy functional and coupling structure.
This deposit contains the paper “A Fully Worked Variational Dissipative–Conservative µ–Ψ Coupled Model” by Kevin Ellis Anderson. The paper presents a fully specified partial differential equation model within the Monotonic Informational Substrate (MIST) framework. An explicit free-energy functional is constructed that couples a real dissipative deviation field (µ) to a complex conservative oscillatory field (Ψ). The corresponding evolution equations are derived directly from variational principles using a dissipative–conservative split. The model is intended as a concrete instantiation of previously established structural results rather than a new axiomatic proposal. It demonstrates monotonic free-energy decay, irreversible energy transfer from oscillatory to dissipative degrees of freedom, effective decoherence under coarse-grained descriptions, and emergent localisation and event-like outcomes, all without introducing stochasticity, collapse postulates, or hidden variables. The coupling and functional choices presented are illustrative rather than unique, and the work serves as a technical example showing how irreversible behaviour and classical definiteness can arise within a deterministic, variational framework.
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