https://doi.org/10.1140/epjc/s10052-026-15490-w
Regular Article - Theoretical Physics
Krylov complexity of thermal state in early universe
Department of Physics, College of Physics, Mechanical and Electrical Engineering, Jishou University, 416000, Jishou, China
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Received:
19
December
2024
Accepted:
24
February
2026
Published online:
13
March
2026
Abstract
Thermal interactions are ubiquitous in the cosmos, driving systems toward equilibrium. In this work, we investigate the evolution of thermal states across the early universe, encompassing the inflationary, radiation-dominated (RD), and matter-dominated (MD) eras, through the lens of Krylov complexity. Utilizing a purification scheme, we map the thermal state to a two-mode pure state, facilitating an open-system analysis of Krylov complexity in contrast to closed-system methodologies. Our numerical results demonstrate that Krylov complexity grows exponentially during inflation, indicating chaotic behavior, before saturating at nearly constant values in the RD and MD eras due to particle production via preheating. Furthermore, we analyze the Krylov entropy, which exhibits an evolutionary trend analogous to that of complexity. Crucially, our analysis reveals a dynamical transition in the universe’s dissipative nature: with the universe acting as a strongly dissipative system during inflation and transitioning to a weakly dissipative regime in the subsequent eras. These findings provide a novel quantum information perspective on early universe dynamics.
© The Author(s) 2026
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