Quantum Markovian Dynamics from a Double Covariance Stochastic Framework

• URL: http://arxiv.org/abs/2605.29508v1
• Date: Thu, 28 May 2026 07:30:55 GMT
• Title: Quantum Markovian Dynamics from a Double Covariance Stochastic Framework
• Abstract summary: macroscopic quantum dynamics emerge through coarse-graining of correlated microscopic fluctuations.<n>We show that the emergent macroscopic dynamics has the exact Gorini-Kossakowski-Sudarshan-Lindblad form.<n>In the fluctuation-free limit, the model reduces naturally to the standard von Neumann equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop an interacting extension of the Double Covariance Model (DCM), a stochastic subquantum framework in which macroscopic quantum dynamics emerge through coarse-graining of correlated microscopic fluctuations. Starting from local stochastic differential equations on subsystem Hilbert spaces, we derive a closed evolution equation for a coarse-grained double covariance operator using multi-scale Itô calculus and sliding-window averaging. The construction explicitly incorporates two separated temporal scales: a fast microscopic fluctuation scale governing subquantum stochastic processes and a slower macroscopic observation scale associated with coarse-grained dynamics. Within the hydrodynamic limit, where the ratio between microscopic correlation time and averaging-window scale vanishes, rapidly fluctuating corrections disappear and the effective dynamics converges to a deterministic macroscopic transport equation. We show that the emergent macroscopic dynamics has the exact Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form: coherent Hamiltonian evolution arises from deterministic subquantum flow, while dissipative channels emerge from quadratic noise correlations. The framework further demonstrates how non-separable interaction Hamiltonians can arise from strictly local, state-dependent stochastic feedback fields. In the fluctuation-free limit, the model reduces naturally to the standard von Neumann equation, providing a unified stochastic foundation for both open and closed quantum dynamics.

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