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arXiv · 2606.19510

Exact Markovian Dissipation Requires Singular Energy Resources

Hiroki Nakabayashi
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Abstract

The Gorini--Kossakowski--Lindblad--Sudarshan (GKLS) equation describes irreversible quantum dynamical semigroups. We show that this description cannot be exact under physically regular energy conditions. We prove that the open-system survival probability under physically regular energy conditions has sublinear decay, whereas any dissipative GKLS semigroup has a linear short-time decay. Hence exact Markovian dissipation requires singular energy resources: an unbounded-below total Hamiltonian or infinite initial energy, and a divergent interaction-energy moment. Therefore, a dissipative time-independent GKLS equation should be regarded as an effective description rather than the exact reduced dynamics of a Hamiltonian dilation satisfying physically regular energy conditions.

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Hiroki Nakabayashi. 2026-06-17. Exact Markovian Dissipation Requires Singular Energy Resources. https://arxiv.org/abs/2606.19510

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