We consider the one dimensional boundary driven harmonic model and its continuous version, both introduced in (Frassek et al. in J Stat Phys 180: 135-171, 2020). By combining duality and integrability the authors of (Frassek and Giardina in J Math Phys 63: 103301, 2022) obtained the invariant measures in a combinatorial representation. Here we give an integral representation of the invariant measures which turns out to be a convex combination of inhomogeneous product of geometric distributions for the discrete model and a convex combination of inhomogeneous product of exponential distributions for the continuous one. The mean values of the geometric and of the exponential variables are distributed according to the order statistics of i.i.d. uniform random variables on a suitable interval fixed by the boundary sources. The result is obtained solving exactly the stationary condition written in terms of the joint generating function. The method has an interest in itself and can be generalized to study other models. We briefly discuss some applications.

Solvable Stationary Non Equilibrium States / Carinci, G.; Franceschini, C.; Gabrielli, D.; Giardinà, C.; Tsagkarogiannis, D.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 191:1(2024), pp. 1-10. [10.1007/s10955-023-03226-z]

Solvable Stationary Non Equilibrium States

Carinci G.;Franceschini C.
;
Giardinà C.;
2024

Abstract

We consider the one dimensional boundary driven harmonic model and its continuous version, both introduced in (Frassek et al. in J Stat Phys 180: 135-171, 2020). By combining duality and integrability the authors of (Frassek and Giardina in J Math Phys 63: 103301, 2022) obtained the invariant measures in a combinatorial representation. Here we give an integral representation of the invariant measures which turns out to be a convex combination of inhomogeneous product of geometric distributions for the discrete model and a convex combination of inhomogeneous product of exponential distributions for the continuous one. The mean values of the geometric and of the exponential variables are distributed according to the order statistics of i.i.d. uniform random variables on a suitable interval fixed by the boundary sources. The result is obtained solving exactly the stationary condition written in terms of the joint generating function. The method has an interest in itself and can be generalized to study other models. We briefly discuss some applications.
2024
191
1
1
10
Solvable Stationary Non Equilibrium States / Carinci, G.; Franceschini, C.; Gabrielli, D.; Giardinà, C.; Tsagkarogiannis, D.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 191:1(2024), pp. 1-10. [10.1007/s10955-023-03226-z]
Carinci, G.; Franceschini, C.; Gabrielli, D.; Giardinà, C.; Tsagkarogiannis, D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1339433
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