Generalized immediate exchange models and their symmetries

Redig, Frank; Sau, Federico

doi:10.1016/j.spa.2017.02.005

Cited by 4 publications

(1 citation statement)

References 10 publications

(23 reference statements)

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“…e.g. [ 17 ]). Also in this inhomogeneous setting the self-duality functions factorize over sites and the stationary measures are in product form, with site-dependent single-site duality functions, resp.…”

Section: Relation Between Simple Factorized Duality Functions and Stamentioning

confidence: 99%

Factorized Duality, Stationary Product Measures and Generating Functions

Redig

2018

J Stat Phys

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We find all self-duality functions of the form for a class of interacting particle systems. We call these duality functions of simple factorized form. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion processes, as well as duality and self-duality functions for their continuous counterparts. The approach is based on, firstly, a general relation between factorized duality functions and stationary product measures and, secondly, an intertwining relation provided by generating functions. For the interacting particle systems, these self-duality and duality functions turn out to be generalizations of those previously obtained in Giardinà et al. (J Stat Phys 135:25–55, 2009 ) and, more recently, in Franceschini and Giardinà (Preprint, arXiv:1701.09115 , 2016 ) . Thus, we discover that only these two families of dualities cover all possible cases. Moreover, the same method discloses all simple factorized self-duality functions for interacting diffusion systems such as the Brownian energy process, where both the process and its dual are in continuous variables.

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Section: Relation Between Simple Factorized Duality Functions and Stamentioning

confidence: 99%

Factorized Duality, Stationary Product Measures and Generating Functions

Redig

2018

J Stat Phys

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On a Class of Solvable Stationary Non Equilibrium States for Mass Exchange Models

Capanna,

Gabrielli,

Tsagkarogiannis

2024

J Stat Phys

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We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of reversible models for which the product invariant measure is known and the gradient condition is satisfied so that we can explicitly compute the transport coefficients associated to the diffusive hydrodynamic rescaling. Based on the Macroscopic Fluctuation Theory (Bertini et al. in Rev Mod Phys 87:593–636, 2015) we have that the large deviations rate functional for a stationary non equilibrium state can be computed solving a Hamilton–Jacobi equation depending only on the transport coefficients and the details of the boundary sources. Thus, we are able to identify a class of models having transport coefficients for which the Hamilton–Jacobi equation can indeed be solved. We give a complete characterization in the case of generalized zero range models and discuss several other cases. For the generalized zero range models we identify a class of discrete models that, modulo trivial extensions, coincides with the class discussed in Frassek and Giardinà (J Math Phys 63(10):103301–103335, 2022) and a class of continuous dynamics that coincides with the class in Franceschini et al. (J Math Phys 64(4): 043304–043321, 2023). Along the discussion we obtain a complete characterization of reversible misanthrope processes solving the discrete equations in Cocozza-Thivent (Z Wahrsch Verw Gebiete 70(4):509–523, 1985).

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Integrable heat conduction model

Franceschini

Frassek

Giardinà

2023

Journal of Mathematical Physics

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We consider a stochastic process of heat conduction where energy is redistributed along a chain between nearest neighbor sites via an improper beta distribution. Similar to the well-known Kipnis–Marchioro–Presutti (KMP) model, the finite chain is coupled at its ends with two reservoirs that break the conservation of energy when working at different temperatures. At variance with KMP, the model considered here is integrable, and one can write in a closed form the n-point correlation functions of the non-equilibrium steady state. As a consequence of the exact solution one, can directly prove that the system is in “local equilibrium,” which is described at the macro-scale by a product measure. Integrability manifests itself through the description of the model via the open Heisenberg chain with non-compact spins. The algebraic formulation of the model allows us to interpret its duality relation with a purely absorbing particle system as a change of representation.

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Generalized immediate exchange models and their symmetries

Cited by 4 publications

References 10 publications

Factorized Duality, Stationary Product Measures and Generating Functions

Factorized Duality, Stationary Product Measures and Generating Functions

On a Class of Solvable Stationary Non Equilibrium States for Mass Exchange Models

Integrable heat conduction model

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