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arXiv:2511.09758

Local arrows of time in quantum many-body systems

Andrew G. Yates, Jordan Cotler, Nishad Maskara, Mikhail D. Lukin

quant-phcond-mat.str-elSubmitted Nov 12, 2025• Announced Nov 14, 2025• 0 citations
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Abstract

We demonstrate that in quantum many-body systems, local arrows of time can differ from the global time $t$ induced by Hamiltonian evolution. That is, within a quantum many-body system, the flow of time can be relative to each observer or by proxy each local subsystem. We provide a definition of local arrows of time in quantum many-body systems, and explain their relation to spacetime quantum entropies. Then we give a variety of numerical and analytical examples which explore different ways in which local arrows of time can manifest in quantum many-body dynamics, including exotic arrows of time arising from quantum thermalization and quantum error correction.

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18+8 pages, 5 figures

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We demonstrate that in quantum many-body systems, local arrows of time can differ from the global time ttt induced by Hamiltonian evolution. That is, within a quantum many-body system, the flow of time can be relative to each observer or by proxy each local subsystem. We provide a definition of local arrows of time in quantum many-body systems, and explain their relation to spacetime quantum entropies. Then we give a variety of numerical and analytical examples which explore different ways in which local arrows of time can manifest in quantum many-body dynamics, including exotic arrows of time arising from quantum thermalization and quantum error correction.
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This work investigates the fundamental connection between quantum mechanics and thermodynamics through the concept of the arrow of time. While the second law of thermodynamics identifies the arrow of time with the monotonic increase of entropy in isolated systems, closed quantum systems evolve unitarily and conserve von Neumann entropy, making the origin of irreversibility less apparent. Here we establish a no-go theorem proving that correlations in unknown states of closed quantum systems cannot be universally removed by any physical operation. This result demonstrates that correlation generation is inherently irreversible, providing a microscopic and universal basis for the arrow of time. In thermodynamic settings, this irreversibility ensures that heat flows spontaneously from hotter to colder subsystems, reproducing the Clausius formulation of the second law. More generally, the irreversible growth of correlations explains entropy increase, the approach to equilibrium, and decoherence as observable manifestations of the same principle. Our findings ground a quantum-mechanical foundation for the second law of thermodynamics and demonstrate the universality of the arrow of time.
The set-theory twist of quantum mechanics uncovers forcing in axiomatic Zermelo-Fraenkel set theory as a viable tool to understand the singularities in a physical spacetime and serves as a link between the quantum and classical worlds. The random forcing explains the emergence of time in quantum mechanics on infinite-dimensional Hilbert spaces. A natural flow of randomness from fully random to deterministic and classical, as in the measurement procedure and the decoherence process, becomes responsible for the cosmological arrow of time and also for the local-coordinate time in spacetime.