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Renormalization group in far-from-equilibrium states

Vladimir Rosenhaus1 and Michael Smolkin2

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Phys. Rev. D 113, 125019 – Published 15 June, 2026

DOI: https://doi.org/10.1103/5spw-kk76

Abstract

We study renormalization group (RG) flows in far-from-equilibrium states. The study is made tractable by focusing on states that are spatially homogeneous, time independent, and scale invariant. Such states, in which mode k has occupation numbers nk∼k−γ, are well known in nonlinear physics. RG flow in such states is qualitatively different from that in the vacuum—a positive γ decreases the dimension of an operator, turning marginal interactions into relevant interactions. We compute one-loop beta functions. Depending on the sign of the beta function, backreaction may either cause a minor shift of the state in the IR or completely change the nature of the state. Focusing on nearly marginal interactions, we construct an analog of the epsilon expansion and IR fixed points, with epsilon now set by the scaling of the interaction rather than the spacetime dimension. In the language of RG flow, critical balance scaling—which has applications in fields as varied as astrophysics and ocean waves—corresponds to the state dynamically adjusting itself along the RG flow until the interaction becomes marginal.

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Phys. Rev. D 113, 125019– Published 15 June, 2026
  • Received 26 December 2025
  • Accepted 29 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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