A quasi-potential for conservation laws with boundary conditions, eprint arXiv:1010, p.3624, 2010. ,
Inequivalence of Ensembles in a System with Long-Range Interactions, Physical Review Letters, vol.59, issue.3, pp.30601-30602, 2001. ,
DOI : 10.1103/PhysRevE.59.2746
Variational convergence of multidimensional conservation laws, Bulletin of the Greek Mathematical Society, vol.57, pp.31-45, 2010. ,
?? -Entropy Cost for Scalar Conservation Laws, Archive for Rational Mechanics and Analysis, vol.39, issue.1, pp.261-309, 2010. ,
DOI : 10.1007/978-3-642-84371-6
URL : http://arxiv.org/pdf/0712.1198
Mesoscopic theory for fluctuating active nematics, New Journal of Physics, vol.15, issue.8, p.85032, 2013. ,
DOI : 10.1088/1367-2630/15/8/085032
URL : https://hal.archives-ouvertes.fr/cea-01478872
Boltzmann and hydrodynamic description for self-propelled particles, Physical Review E, vol.63, issue.2, p.22101, 2006. ,
DOI : 10.1088/0022-3719/6/7/010
URL : https://hal.archives-ouvertes.fr/hal-00910408
Macroscopic fluctuation theory, Reviews of Modern Physics, vol.2005, issue.2, p.593, 2015. ,
DOI : 10.1088/1751-8113/41/50/505001
URL : http://arxiv.org/abs/1404.6466
Large deviations principles for non gradient weakly asymmetric stochastic lattice gases Ann, Appl. Prob, vol.23, issue.1, pp.1-65, 2013. ,
DOI : 10.1214/11-aap805
URL : http://arxiv.org/abs/1011.1082
Distribution of current in nonequilibrium diffusive systems and phase transitions, Physical Review E, vol.72, issue.6, p.66110, 2005. ,
DOI : 10.1103/PhysRevE.52.3512
URL : https://hal.archives-ouvertes.fr/hal-00018380
Current Large Deviations for Asymmetric Exclusion Processes with Open Boundaries, Journal of Statistical Physics, vol.72, issue.3, pp.277-300, 2006. ,
DOI : 10.1007/978-3-642-84371-6
URL : https://hal.archives-ouvertes.fr/hal-00085457
Résolution d'´ equations d'´ evolution quasilinéaires en dimension N d'espacè a l'aide d'´ equations linéaires en dimension N + 1, J. Differential Equations, vol.50, issue.375, p.390, 1983. ,
Hyperbolic conservation laws in continuum physics, 2016. ,
DOI : 10.1007/978-3-662-49451-6
An introduction to ?-convergence. Progress in Nonlinear Differential Equations and their Applications, p.340, 1993. ,
Scalar conservation laws with stochastic forcing, Journal of Functional Analysis, vol.259, issue.4, pp.1014-1042, 2010. ,
DOI : 10.1016/j.jfa.2010.02.016
URL : https://hal.archives-ouvertes.fr/hal-00451641
: Helium, antiferromagnets, and liquid-gas systems, Physical Review B, vol.83, issue.1, p.353, 1978. ,
DOI : 10.1016/0550-3213(74)90271-5
CONTINUUM LIMIT OF SELF-DRIVEN PARTICLES WITH ORIENTATION INTERACTION, Mathematical Models and Methods in Applied Sciences, vol.18, issue.supp01, pp.1193-1215, 2008. ,
DOI : 10.1002/cpa.20027
URL : https://hal.archives-ouvertes.fr/hal-00635078
Non equilibrium Thermodynamics, 1984. ,
Large deviations techniques and applications. Stochastic Modelling and Applied Probability, p.396, 2010. ,
Large Deviations. Fields Institute Monographs, 2008. ,
Large fluctuations for a nonlinear heat equation with noise, Journal of Physics A: Mathematical and General, vol.15, issue.10, pp.3025-3055, 1982. ,
DOI : 10.1088/0305-4470/15/10/011
Stochastic scalar conservation laws, Journal of Functional Analysis, vol.255, issue.2, pp.313-373, 2008. ,
DOI : 10.1016/j.jfa.2008.02.004
URL : http://doi.org/10.1016/j.jfa.2008.02.004
Random Perturbations of Dynamical Systems, Grundlehren der Mathematischen Wissenschaften, 2012. ,
DOI : 10.1007/978-1-4612-0611-8
On the (Boltzmann) entropy of non-equilibrium systems, Physica D: Nonlinear Phenomena, vol.193, pp.1-4, 2004. ,
Long-range correlations for conservative dynamics, Physical Review A, vol.44, issue.4, pp.1954-968, 1990. ,
DOI : 10.1007/BF01011311
Macroscopic potentials, bifurcations and noise in dissipative systems, Noise in Nonlinear Dynamical Systems, 1989. ,
Solving the KPZ equation, Annals of Mathematics, vol.178, issue.2, pp.559-664, 2013. ,
DOI : 10.4007/annals.2013.178.2.4
Theory of dynamic critical phenomena, Reviews of Modern Physics, vol.30, issue.88, p.435, 1977. ,
DOI : 10.1103/PhysRevLett.30.22
Symmetries in fluctuations far from equilibrium, Proc. Natl. Acad. Sci. USA, pp.7704-7709, 2011. ,
DOI : 10.1038/nature04061
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3093531
The asymmetric exclusion process in one dimension, 2000. ,
Prigogine ModernThermodynamics: From Heat Engines to Dissipative Structures, 1998. ,
Diffusion Constants near the Critical Point for Time-Dependent Ising Models. I, Physical Review, vol.69, issue.1, p.224, 1966. ,
DOI : 10.1103/PhysRev.139.A1866
On a stochastic scalar conservation law, Indiana University Mathematics Journal, vol.52, issue.1, pp.227-256, 2003. ,
DOI : 10.1512/iumj.2003.52.2310
URL : http://doi.org/10.1512/iumj.2003.52.2310
Course of theoretical physics, Fluid Mechanics, 1987. ,
Structure of Entropy Solutions for Multi-Dimensional Scalar Conservation Laws, Archive for Rational Mechanics and Analysis, vol.170, issue.2, pp.137-184, 2003. ,
DOI : 10.1007/s00205-003-0270-9
A kinetic formulation of multidimensional scalar conservation laws and related questions, J. AMS, vol.7, pp.169-191, 1994. ,
On the Origin and the Use of Fluctuation Relations for the Entropy, Sem Poncaré, vol.2, 2003. ,
DOI : 10.1007/978-3-0348-7932-3_8
Anisotropic perturbations of the simple symmetric exclusion process : long range correlations, Journal de Physique I, vol.1, issue.5, pp.669-684, 1991. ,
DOI : 10.1051/jp1:1991161
URL : https://hal.archives-ouvertes.fr/jpa-00246361
Large deviations principles for stochastic scalar conservation laws. Probab. Theory Relat, pp.607-648, 2010. ,
DOI : 10.1007/s00440-009-0218-6
Fluctuations and Irreversible Processes, Physical Review, vol.7, issue.6, p.1505, 1953. ,
DOI : 10.1143/JPSJ.7.439
dimensions, Physical Review E, vol.93, issue.4, p.40103, 2016. ,
DOI : 10.1088/1742-5468/2005/08/P08003
Kinetic formulation of conservation laws, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-01146188
A kinetic equation with kinetic entropy functions for scalar conservation laws, Communications in Mathematical Physics, vol.81, issue.3, pp.501-517, 1991. ,
DOI : 10.1007/BF02099071
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.725
Hydrodynamic limit for attractive particle systems on 417-1417-1417-1, Communications in Mathematical Physics, vol.58, issue.3, pp.417-448, 1991. ,
DOI : 10.1007/978-1-4613-8542-4
Systems of conservation laws. 1. Hyperbolicity, entropies, shock waves. Translated from the 1996 French original by I. N. Sneddon, p.263, 1999. ,
URL : https://hal.archives-ouvertes.fr/ensl-01402415
Large scale dynamics of interacting particle systems, 1999. ,
On the probability functional of diffusion processes (in Russian) English translation, Proc. Sixth All-Unian Conf. Theory Prob. and Math. Statist, pp.471-483, 1962. ,
On the structure of the optimal path to a fluctuation Phys, Rev. E, vol.95, p.32119, 2017. ,
Order and symmetry-breaking in the fluctuations of driven systems, arXiv preprint arXiv, pp.1606-07507, 2016. ,
Simple spin models with non-concave entropies, American Journal of Physics, vol.76, issue.1, pp.10-1119, 2008. ,
DOI : 10.1119/1.2794350
URL : http://arxiv.org/abs/cond-mat/0504020
Large deviations and applications. CBMS-NSF Regional Conference Series in Applied Mathematics, 46, Society for Industrial and Applied Mathematics (SIAM), p.75, 1984. ,
DOI : 10.1007/bfb0086178
Large deviations for the asymmetric simple exclusion process Stochastic analysis on large scale interacting systems, Adv. Stud. Pure Math. Math. Soc. Japan, vol.39, pp.1-27, 2004. ,
Quantum Field Theory and Critical Phenomena, International Series of Monographs on Physics, vol.113, 2002. ,
DOI : 10.1093/acprof:oso/9780198509233.001.0001
URL : https://hal.archives-ouvertes.fr/hal-00120423
Fédération Denis Poisson, Université d'Orléans, Collegium Sciences et Techniques, Bâtiment de mathématiques -Route de Chartres, pp.6759-45067 ,
mail address: julien.barre@univ-orleans.fr Université Côte d'Azur, CNRS, LJAD, Parc Valrose, 06108 NICE Cedex 02, France E-mail address: cbernard@unice.fr Université Côte d ,