On the emergence of quantum mechanics from stochastic processes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912983496523776 |
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| author | Doukas, Jason |
| author_facet | Doukas, Jason |
| contents | The stochastic--quantum correspondence reinterprets quantum dynamics as arising from an underlying stochastic process on a configuration space. We generalize the correspondence by lifting an arbitrary stochastic kernel $Γ$ in finite dimension to a map $ϕ$ on $B(\mathcal H)$, formulating the associated lift-compatibility relation, and giving an explicit dictionary between $Γ$ and CPTP (Kraus) maps. We isolate Chapman--Kolmogorov divisibility of the lifted family as the decisive additional constraint: when a CK-consistent CPTP family exists, the lift admits a Lindblad master equation form. In this picture, off-diagonal (phase) degrees of freedom act as a compressed carrier of history dependence not fixed by transition kernels alone; conversely, the apparent emergence of quantum phase information from a phase-blind stochastic description is explained as a memory effect. Finally, we state and prove a divisibility criterion for the underlying stochastic kernels, expressed as a condition involving divisibility of the lifted map together with a diagonality requirement on the density operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22095 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the emergence of quantum mechanics from stochastic processes Doukas, Jason Quantum Physics The stochastic--quantum correspondence reinterprets quantum dynamics as arising from an underlying stochastic process on a configuration space. We generalize the correspondence by lifting an arbitrary stochastic kernel $Γ$ in finite dimension to a map $ϕ$ on $B(\mathcal H)$, formulating the associated lift-compatibility relation, and giving an explicit dictionary between $Γ$ and CPTP (Kraus) maps. We isolate Chapman--Kolmogorov divisibility of the lifted family as the decisive additional constraint: when a CK-consistent CPTP family exists, the lift admits a Lindblad master equation form. In this picture, off-diagonal (phase) degrees of freedom act as a compressed carrier of history dependence not fixed by transition kernels alone; conversely, the apparent emergence of quantum phase information from a phase-blind stochastic description is explained as a memory effect. Finally, we state and prove a divisibility criterion for the underlying stochastic kernels, expressed as a condition involving divisibility of the lifted map together with a diagonality requirement on the density operator. |
| title | On the emergence of quantum mechanics from stochastic processes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.22095 |