# Illinois Physicists Propose Framework for Classifying Non-Equilibrium Quantum Phases

- Published: 2026-11-06 23:51 UTC
- Section: Science › Physics
- Tags: quantum phases, topological states, mixed states, non-equilibrium systems, Illinois physicists
- URL: https://realtech.media/news/rt-232fd904e5b9677e17d40822_illinois_physicists_propose/

**A new framework for classifying non-equilibrium quantum phases of matter has been developed, addressing challenges in understanding open quantum systems.**

![Illinois Physicists Propose Framework for Classifying Non-Equilibrium Quantum Phases](https://realtech.media/media/2026/11/97ddd0d509119b45.jpg)
*UCL Mathematical & Physical Sciences from London, UK, Wikimedia Commons, CC BY 2.0*

Illinois physicists at the Anthony J. Leggett Institute for Condensed Matter Theory have proposed a new framework for classifying non-equilibrium quantum phases of matter, published in *Physical Review X*. This work addresses the challenges of categorizing open quantum systems, which interact freely with their environment, and overcomes limitations of existing classification methods.

The researchers introduced three axioms: local recoverability, absence of long-range correlations, and spatial uniformity. States satisfying these axioms are considered fixed points, and the framework promotes these fixed points to equivalence classes, or phases. This marks a significant step towards a systematic classification of mixed-state phases of matter.

From these axioms, a rich set of topological data emerges, which is crucial for distinguishing between different mixed-state phases. The study reveals that each topological mixed state supports locally indistinguishable classical and/or quantum logical memories, responding uniquely to topological operations. Furthermore, the researchers identified a hierarchy of secret-sharing constraints in non-Abelian phases, where reliable recovery of information requires specific coordination among spatial subregions.

Large-scale numerical simulations were conducted to validate the stability of the proposed framework. The results showed that weakly decohered fixed points respect the axioms after coarse-graining, and the axiom violations exhibit a critical point crossing, facilitating its identification without ambiguity. These findings lay the groundwork for a comprehensive classification of topological states in open quantum systems.

## Sources

1. [Physical Review X](https://doi.org/10.1103/3bpt-f9pd)
2. [newswise.com](https://www.newswise.com/articles/classifying-non-equilibrium-phases-of-matter)

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Source: RealTech, realtech.media — https://realtech.media/news/rt-232fd904e5b9677e17d40822_illinois_physicists_propose/