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  • Open Access

Conservative dissipation shapes symmetry breaking in nonequilibrium currents

Matteo Sireci1,2,*, Luca Peliti3,†, and Daniel Maria Busiello4,5,‡

  • *Contact author: matteo.sireci@phys.ens.fr
  • †Contact author: luca@peliti.org
  • ‡Contact author: danielmaria.busiello@unipd.it
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Phys. Rev. Research 8, 033126 – Published 30 July, 2026

DOI: https://doi.org/10.1103/4rsq-ybmk

Abstract

Most natural thermodynamic systems operate far from equilibrium, developing persistent currents and organizing into nonequilibrium stationary states (NESSs). Yet, the general principles governing how nonequilibrium driving reshapes probability distributions and breaks equilibrium symmetries remain poorly understood. Here, we establish a geometric framework connecting dissipation, current organization, and symmetry breaking in mesoscopic stochastic systems governed by Langevin dynamics. Using the inverse diffusion matrix as a metric, we derive the general geometric properties of stationary current velocities, employing a small-noise expansion to obtain further insights on their link to symmetry breaking. We then introduce a nonorthogonal decomposition of the velocity field into conservative and nonconservative components. The nonconservative contribution quantifies the violation of detailed balance induced by external driving, while the conservative one measures how the system reorganizes its internal state space relative to a reference equilibrium distribution. This decomposition naturally induces a splitting of entropy production and leads to an exact balance relation together with bounds defining the accessible thermodynamic region of a NESS. We show that the conservative contribution determines how nonequilibrium conditions amplify or generate symmetry-breaking phenomena, yielding a geometric classification of NESSs. We apply the framework to systems ranging from molecular machines to coupled oscillators and Brownian gyrators, and extend it to multiplicative-noise dynamics, where additional symmetry breaking emerges from curvature induced by space-dependent diffusion. Our results uncover a general connection between geometry, dissipation, and emergent organization in nonequilibrium thermodynamics.

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Phys. Rev. Research 8, 033126– Published 30 July, 2026
  • Received 12 September 2025
  • Accepted 26 June 2026
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