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arXiv · 2606.08595

Is Exact Markovianity Fundamental Once Time Is Relational?

Partha Nandi·Francesco Petruccione
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Abstract

Markovian open quantum theory assumes evolution with respect to an external classical time parameter, yet no preferred notion of time exists fundamentally in relativistic physics. We resolve this tension by formulating relativistic open quantum dynamics relationally through finite-resolution quantum clocks. Using the Schwinger-Tomonaga formalism, we derive a covariant master equation directly on spacetime hypersurfaces and show that the resulting reduced dynamics is generically non-Markovian even for local interactions. Environmental correlations and clock fluctuations jointly generate the memory kernel, while the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) structure emerges only after relational coarse-graining, implying that exact Markovian evolution is effective rather than fundamental. In the sharp-clock limit, the formalism reduces to the Anastopoulos-Hu gravitational decoherence equation.

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Partha Nandi, Francesco Petruccione. 2026-06-07. Is Exact Markovianity Fundamental Once Time Is Relational?. https://arxiv.org/abs/2606.08595

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