Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1705.03833

Eliminating the cuspidal temperature profile of a non-equilibrium chain

Michael M. Cândido·Welles A. M. Morgado·Sílvio M. Duarte Queirós
View original source ↗Read source document ↗Export metadata ↓

Abstract

In 1967, Z. Rieder, J. L. Lebowitz and E. Lieb (RLL) introduced a model of heat conduction on a crystal that became a milestone problem of non-equilibrium statistical mechanics. Along with its inability to reproduce Fourier's Law - which subsequent generalizations have been trying to amend - the RLL model is also characterized by awkward cusps at the ends of the non-equilibrium chain, an effect that has endured all these years without a satisfactory answer. In this paper, we first show that such trait stems from the insufficiency of pinning interactions between the chain and the substrate. Assuming the possibility of pinning the chain, the analysis of the temperature profile in the space of parameters reveals that for a proper combination of the border and bulk pinning values, the temperature profile may shift twice between the RLL cuspidal behavior and the expected monotonic local temperature evolution along the system, as a function of the pinning. At those inversions, the temperature profile along the chain is characterized by perfect plateaux: at the first threshold, the cumulants of the heat flux reach their maxima and the vanishing of the two-point velocity correlation function for all sites of the chain so that the system behaves similarly to a "phonon box". On the other hand, at the second change of the temperature profile, we still have the vanishing of the two-point correlation function but only for the bulk, which explains the emergence of the temperature plateau and thwarts the reaching of the maximal values of the cumulants of the heat flux.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

BibTeXRIS

Michael M. Cândido, Welles A. M. Morgado, Sílvio M. Duarte Queirós. 2017-05-10. Eliminating the cuspidal temperature profile of a non-equilibrium chain. https://doi.org/10.1007/s13538-017-0494-z

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

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗
arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗
arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗