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2021 Hydrodynamic limit for a chain with thermal and mechanical boundary forces
Tomasz Komorowski, Stefano Olla, Marielle Simon
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Electron. J. Probab. 26: 1-49 (2021). DOI: 10.1214/21-EJP581


We prove the hydrodynamic limit for a one dimensional harmonic chain with a random flip of the momentum sign. The system is open and subject to two thermostats at the boundaries and to an external tension at one of the endpoints. Under a diffusive scaling of space-time, we prove that the empirical profiles of the two locally conserved quantities, the volume stretch and the energy, converge to the solution of a non-linear diffusive system of conservative partial differential equations.

Funding Statement

This work was partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.
T.K. acknowledges the support of NCN grant UMO2016/23/B/ST1/00492. S.O. acknowledges the support of the ANR-15-CE40-0020-01 grant LSD, M.S. thanks Labex CEMPI (ANR-11-LABX-0007-01), and the ANR grant MICMOV (ANR-19-CE40-0012) of the French National Research Agency (ANR)


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Tomasz Komorowski. Stefano Olla. Marielle Simon. "Hydrodynamic limit for a chain with thermal and mechanical boundary forces." Electron. J. Probab. 26 1 - 49, 2021.


Received: 18 April 2020; Accepted: 10 January 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-EJP581

Primary: 60K35 , 82C70

Keywords: boundary conditions , Fourier-Wigner functions , harmonic chain , Hydrodynamic limit


Vol.26 • 2021
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