Hamiltonian curl-forces in systems coupled to multiple thermal reservoirs

Omer Chor; Aljaž Godec; Oren Raz

Home/Archive/arXiv

arXiv · 2610.08423

Hamiltonian curl-forces in systems coupled to multiple thermal reservoirs

Omer Chor·Aljaž Godec·Oren Raz

View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the statistical mechanics of a system coupled to multiple heat reservoirs at different temperatures, a setting which typically sustains nontrivial circulation. By applying a canonical transformation, we map the system onto that of a particle coupled to a single reservoir yet driven by a deterministic curl-force---a reversible, velocity-independent non-conservative force with non-vanishing curl---that can be described by a Hamiltonian with an anisotropic kinetic energy term. Despite the Hamiltonian structure, the system does not relax to the corresponding Boltzmann distribution, and is genuinely out of equilibrium. The mapping provides a mechanical interpretation of the currents in multi-temperature systems, as we demonstrate by means of two examples. In particular, the direction of circulation is qualitatively predictable from the deterministic force field. For the exactly solvable case of an $N$-dimensional underdamped Ornstein-Uhlenbeck process, we derive explicit expressions for the steady-state distribution and the entropy production rate, highlighting the role of the (generalized) curl of the force field in driving the system out of thermal equilibrium. Finally, we show how a non-conservative force can be used to exactly equilibrate any system coupled to multiple reservoirs, and obtain the corresponding equilibrium distribution.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Omer Chor, Aljaž Godec, Oren Raz. 2026-10-06. Hamiltonian curl-forces in systems coupled to multiple thermal reservoirs. https://arxiv.org/abs/2610.08423

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Edge Currents Shape Condensates in Chiral Active Matter

Chiral active matter, which breaks both parity symmetry and time-reversal symmetry, is ubiquitous in living systems. Here, we introduce a minimal two-dimensional chiral active lattice gas by incorporating stochastic, biased local rotations. At low temperatures, the system coarsens into condensates with chiral orientations and faceted, crystal-like shapes. The interfaces align at characteristic angles with respect to the lattice axes and exhibit edge currents that are persistent, unidirectional, and angle-dependent. To generalise these findings, we propose a continuum theory by adding an active chiral edge current term to Model B, which reveals the essential role of active chiral transport in the interfacial dynamics of phase separation. Edge currents with $n$-fold symmetry produce condensates whose shapes resemble regular $n$-sided polygons. In the thin-interface limit, we construct an effective interface potential governing edge currents, from which the steady-state condensate geometry can be obtained, both in the lattice model and the continuum description.

cond-mat.stat-mech↗

arXiv2026

Force Geometry and Irreversibility in Nonequilibrium Overdamped Dynamics

Recent experiments have revealed heterogeneous dissipation in optically trapped systems, often anticorrelated with local positional fluctuations, exposing a structural gap in the scalar stochastic thermodynamic description. While the scalar framework successfully quantifies dissipation through currents and entropy production rates, it does not reveal the underlying vectorial force geometry that shapes spatial dissipation patterns. Here, we bridge this gap by identifying force geometry as an organizing principle for nonequilibrium thermodynamics, introducing force alignment as a geometric determinant of irreversibility. We show that entropy production depends not only on force magnitudes but also on the relative orientation between deterministic driving forces and entropic gradients, vanishing only under exact anti-alignment with matched magnitudes. We formalize this geometric alignment through a time-dependent force-correlation coefficient, quantifying the relative orientation between the forces. This yields an instantaneous geometric lower bound on entropy production that remains valid even when force magnitudes are matched. For overdamped dynamics, perfect anti-alignment defines a thermodynamic stall where net transport vanishes and the lower bound on entropy production is saturated. This force-level perspective provides a structural explanation for the experimentally observed fluctuation-dissipation anticorrelation and nonuniform dissipation. We construct geometric control charts for both constant dragging and sinusoidal driving protocols, explicitly locating experimental operating points within this force-space representation. Together, these results position force geometry as a unifying structural perspective on irreversibility, spanning active biological systems, microrheology, and naturally extending to underdamped dynamics.

cond-mat.stat-mech↗

arXiv2026

Tensor-Network Population Annealing

We propose a hybrid sampling method, tensor-network population annealing (TNPA), which combines tensor-network (TN) initialization with population annealing (PA). We apply this method to the two-dimensional Edwards-Anderson Ising spin glass. The approach is motivated by the limitations of existing methods: TN-based samplers can become numerically unstable in frustrated spin systems at low temperatures, whereas conventional PA requires a long annealing schedule when started from the high-temperature limit. In TNPA, TN contractions are used only within a reliable temperature range to generate initial configurations that are close to the equilibrium distribution. The subsequent low-temperature equilibration is then carried out by PA. To stabilize the initialization process, we introduce a diagnostic based on the effective sample size that adaptively selects the initialization temperature. The proposed framework provides a practical and physically motivated route to low-temperature sampling by combining the complementary strengths of TN and PA.

cond-mat.stat-mech↗