Conservative dissipation shapes symmetry breaking in nonequilibrium currents
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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BibTeX
@article{sireci2026conservative,
title = {{Conservative dissipation shapes symmetry breaking in nonequilibrium currents}},
author = {Matteo Sireci and Luca Peliti and Daniel Maria Busiello},
journal = {Physical Review Research},
year = {2026},
month = jul,
doi = {10.1103/4rsq-ybmk},
url = {https://hal.science/hal-05767270v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Conservative dissipation shapes symmetry breaking in nonequilibrium currents
AU - Matteo Sireci
AU - Luca Peliti
AU - Daniel Maria Busiello
PY - 2026
DA - 2026/07/30
JO - Physical Review Research
DO - 10.1103/4rsq-ybmk
UR - https://hal.science/hal-05767270v1
AB - 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.
SN - 2643-1564
SN - 2643-1564
ER -