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arXiv · 2509.08078

(A)Symmetric Complexity and the Quantum Mpemba Effect

Cameron Beetar·Jeff Murugan·Hendrik J. R. van Zyl
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Abstract

The Quantum Mpemba Effect (QME) -- the counter-intuitive phenomenon where states further from equilibrium can relax faster than those closer to it -- challenges standard expectations of quantum thermalization. In this work, we introduce Krylov complexity as a sensitive diagnostic for the QME. We show that Krylov spread complexity encodes the asymmetry essential to the effect, and we define a new class of projective (a)symmetric complexities that sharpen this connection. Strikingly, the structure of these projective complexities at the initial moment ($t=0$) already carries predictive power for the onset of Mpemba-like inversions, obviating the need for explicit time evolution. Our results suggest that the geometry of states in Krylov space captures deep information about non-monotonic relaxation and provides a powerful framework for diagnosing and anticipating anomalous thermalization phenomena in quantum systems.

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Cameron Beetar, Jeff Murugan, Hendrik J. R. van Zyl. 2025-09-09. (A)Symmetric Complexity and the Quantum Mpemba Effect. https://arxiv.org/abs/2509.08078

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