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arXiv:2410.13375 · Physical Review Letters

Dissipation Enables Robust Extensive Scaling of Multipartite Correlations

Krzysztof Ptaszyński, Massimiliano Esposito

Published Jul 8, 2025• 3 citations
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Abstract

We investigate the multipartite mutual information between N discrete-state stochastic units interacting in a network that is invariant under unit permutations. We show that, when the system relaxes to fixed point attractors, multipartite correlations in the stationary state either do not scale extensively with N or the extensive scaling is not robust to arbitrarily small perturbations of the system dynamics. In particular, robust extensive scaling cannot occur in thermodynamic equilibrium. In contrast, mutual information scales extensively when the system relaxes to time-dependent attractors (e.g., limit cycles), which can occur only far from equilibrium. This demonstrates the essential role of dissipation in the generation and maintenance of multipartite correlations. We illustrate our theory with the nonequilibrium Potts model.

DOI
10.1103/j21x-hrsq

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We investigate the multipartite mutual information between N discrete-state stochastic units interacting in a network that is invariant under unit permutations. We show that, when the system relaxes to fixed point attractors, multipartite correlations in the stationary state either do not scale extensively with N or the extensive scaling is not robust to arbitrarily small perturbations of the system dynamics. In particular, robust extensive scaling cannot occur in thermodynamic equilibrium. In contrast, mutual information scales extensively when the system relaxes to time-dependent attractors (e.g., limit cycles), which can occur only far from equilibrium. This demonstrates the essential role of dissipation in the generation and maintenance of multipartite correlations. We illustrate our theory with the nonequilibrium Potts model.
Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to determine the macroscopic behavior of the steady-state multipartite mutual information between N interacting units undergoing Markovian evolution that is invariant under unit permutations. Using this approach, we extend a conclusion previously drawn for classical systems that either the extensive scaling of mutual information is not possible for systems relaxing to fixed points of the mean-field dynamics, or such scaling is not robust to perturbations of system dynamics. In contrast, robust extensive scaling occurs for a system relaxing to time-dependent attractors, e.g., limit cycles. We illustrate the applicability of our method on the driven-dissipative Lipkin-Meshkov-Glick model.
Entanglement equilibration need not mark the end of quantum-information dynamics in quantum thermalization. We show that the complete Schmidt spectra of a fixed tripartition can become stationary while its multipartite correlation structure, distinguished by local-unitary invariants, continues to evolve. This separation occurs exactly within a finite window in self-dual kicked-Ising dynamics and asymptotically in Haar-random circuits. We further demonstrate an independently tunable timescale for multipartite dynamics using quantum-error-correcting codes. When coupled to a locally scrambling bath, ordinary entanglement approaches equilibrium through rapid local scrambling, while weak logical--bath coupling drives a slower reorganization of multipartite correlations. These results reveal a deeper distinction than the ordering of equilibration times: bipartite entanglement and multipartite correlation structure can probe distinct physical channels of quantum-information dynamics, rather than merely different stages of the same relaxation process.
Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to quantum multipartite information dynamics, where both the system and the environment are multipartite without assuming any thermodynamic constraints. Based on the two-point measurement scheme and the classical probability, we establish the fluctuation theorem for the dynamics of classical multipartite mutual information. By extending to quasiprobability, we derive quantum fluctuation theorems for multipartite coherence and quantum correlations, presenting them in both integral and detailed forms. Our theoretical results are illustrated and verified using three-qubit examples, and feasible experimental verification protocols are proposed. These findings uncover the statistical structure underlying the nonequilibrium quantum information dynamics, providing fundamental insights and alternative tools for advancing quantum technologies.
In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles. Unfortunately, its characterization is a formidable task, as non-complementary parts are generally in a mixed state. We show that for integrable systems, this quantum information dynamics can be quantitatively understood within the quasiparticle picture for the entanglement spreading. Precisely, we provide an exact prediction for the time evolution of the logarithmic negativity after a quench. In the space-time scaling limit of long times and large subsystems, the negativity becomes proportional to the Rényi mutual information with Rényi index α = 1 / 2 . We provide robust numerical evidence for the validity of our results for free-fermion and free-boson models, but our framework applies to any interacting integrable system.
A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analog of such a theory. Specifically, we consider local dissipative dynamics preparing an equilibrium steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes, there exist asymptotically stationary symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.
Conditional mutual information (CMI) is a widely studied multipartite correlation measure with a connection to the Markov property. Intriguingly, CMI can be generated by local dissipation, a phenomenon closely related to teleportation. The onset of long-range CMI corresponds to an information-theoretic mixed-state phase transition, with far-ranging implications for phase transitions, decoding, and state compressions. Little is known, however, about the conditions under which dissipation can generate long-range CMI. In this Letter, we provide the first rigorous results in this direction. We establish that CMI in high-temperature commuting Gibbs states subject to local dissipation decays exponentially under certain mild restrictions. Conversely, we show that the same setup can sustain long-range CMI at low temperatures. Our results establish the existence of finite-temperature information-theoretic phase transitions even in models that have no finite-temperature thermodynamic phase transitions.