This paper shows how classical transport dynamics arise naturally from the same variational dissipative–conservative framework that also supports quantum-analogue behaviour. In the transport-dominated regime, the oscillatory field reduces to Hamilton–Jacobi dynamics with well-defined trajectories and effective inertia, while coupling to auxiliary dissipative degrees of freedom suppresses interference and stabilises classical motion. No stochastic noise, no collapse postulates, and no hidden variables are introduced. Quantum, classical, and decoherent behaviour appear as distinct dynamical regimes of a single deterministic system, controlled by the balance between phase transport and amplitude curvature. Classical mechanics is recovered not as a foundational axiom, but as an effective description with a clear domain of validity.
This paper shows how classical transport dynamics arise naturally from the same variational dissipative–conservative framework that also supports quantum-analogue behaviour. In the transport-dominated regime, the oscillatory field reduces to Hamilton–Jacobi dynamics with well-defined trajectories and effective inertia, while coupling to auxiliary dissipative degrees of freedom suppresses interference and stabilises classical motion. No stochastic noise, no collapse postulates, and no hidden variables are introduced. Quantum, classical, and decoherent behaviour appear as distinct dynamical regimes of a single deterministic system, controlled by the balance between phase transport and amplitude curvature. Classical mechanics is recovered not as a foundational axiom, but as an effective description with a clear domain of validity.
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 “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.
We develop a dissipative extension of classical mechanics based on a complex, and more generally quaternionic, action principle that endows every classical system with an intrinsic environment. Decomposing the action into conservative and divergence-induced components yields two coupled Hamilton Jacobi equations describing a dynamically intertwined system environment pair. This motivates a Dual Sector or Dual Environmental Interpretation (DSI/DEI), in which the additional degrees of freedom behave as an image sector exchanging energy, information, and phase with the system. Applying a generalized Madelung transform produces a nonlinear dissipative wave equation whose symmetric equilibrium limit reduces to the Schroedinger equation, with the quantum potential and linearity emerging from balanced intersector coupling. In this framework, the wavefunction is not fundamental but encodes the interaction geometry between system and environment, providing a classical origin for interference, amplitude phase coupling, and probabilistic structure. Extending the imaginary structure to multiple independent directions yields a multienvironment generalization capable of representing measurement-like processes, nonMarkovian memory, and entanglement type correlations. The formulation unifies aspects of dual-system models, hydrodynamic approaches, and non-Hermitian dynamics within a single action-based framework, and suggests that quantum mechanics corresponds to a stable symmetric phase of a broader dissipative classical theory.
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.
We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally imposed randomness. Within the theory of moving manifolds, we establish a curvature-noise correspondence: fluctuations are governed by the inverse curvature tensor, while entropy production is controlled by curvature deformation. The invariant continuity law on a moving hypersurface yields a geometric Fokker-Planck equation, and curvature-velocity coupling generates a quadratic Onsager-Machlup functional determining path weights. The resulting entropy functional satisfies a curvature-driven monotonicity law, providing a geometric derivation of the Second Law. In two dimensions, the curvature invariant reduces to Gaussian curvature and encodes topology, so topological transitions produce discrete entropy jumps. When the ambient space carries a Minkowskian signature, the same curvature-kinetic quadratic form that generates dissipative thermal weights produces oscillatory phase weights, and the Laplace-Beltrami operator governing entropy evolution acquires a Schrödinger-type structure. This provides a geometric resolution of the apparent distinction between classical stochastic behaviour and quantum dynamics. These results show that stochastic behaviour, thermodynamic irreversibility, and quantum transition amplitudes are unified within the moving manifold framework. Geometry does not merely accommodate stochasticity; stochastic behaviour arises as a consequence of deterministic geometric evolution. The theory predicts curvature-controlled anisotropic diffusion, entropy jumps at topology-changing events, and a geometric thermal-quantum crossover in which classical stochastic weights and quantum amplitudes are generated by the same curvature-kinetic action.
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert space theory, a Hilbert space structure is constructed from the Hilbert space formulation of the underlying Hamilton-Randers model and associated with the space of wave functions of quantum mechanical systems. We can prove the emergence of the Born rule from ergodic considerations. A geometric mechanism for a natural spontaneous collapse of the quantum states based on the concentration of measure phenomena as it appears in metric geometry is discussed.We show the existence of stable vacua states for the quantized matter Hamiltonian. Another consequence of the concentration of measure is the emergence of a weak equivalence principle for one of the dynamics of the fundamental degrees of freedom. We suggest that the reduction of the quantum state is driven by a gravitational type interaction. Such interaction appears only in the dynamical domain when localization of quantum observables happens, it must be a classical interaction. We discuss the double slit experiment in the context of the framework proposed, the interference phenomena associated with a quantum system in an external gravitational potential, a mechanism explaining non-quantum locality and also provide an argument in favour of an emergent interpretation of every macroscopic time parameter. Entanglement is partially described in the context of Hamilton-Randers theory and how naturally Bell's inequalities should be violated.