A. Khinchin, The Mathematical Foundations of Statistical Mechanics, 1949.

D. Ruelle, Statistical Mechanics: Rigorous Results; Benjamin: Amsterdam, The Netherlands, 1969.
DOI : 10.1142/4090

R. S. Ellis and . Entropy, Large deviations and statistical mechanics, 1985.
DOI : 10.1090/conm/041/814705

I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, Journal of The Electrochemical Society, vol.110, issue.4, 1967.
DOI : 10.1149/1.2425756

D. Groot, S. Mazur, and P. , Non-Equilibrium Thermodynamics, 2011.

B. Derrida, Non-equilibrium steady states: fluctuations and large deviations of the density and of the current, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.07, pp.10-1088, 2007.
DOI : 10.1088/1742-5468/2007/07/P07023

T. Chou, K. Mallick, and R. K. Zia, Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport, Reports on Progress in Physics, vol.74, issue.11, pp.74-116601, 2011.
DOI : 10.1088/0034-4885/74/11/116601

M. D. Donsker and S. R. Varadhan, Asymptotic evaluation of certain markov process expectations for large time, I, Communications on Pure and Applied Mathematics, vol.XIX, issue.3, pp.1-47, 1975.
DOI : 10.1002/cpa.3160280102

M. D. Donsker and S. R. Varadhan, Asymptotic evaluation of certain markov process expectations for large time, II, Communications on Pure and Applied Mathematics, vol.28, issue.2, pp.279-301, 1975.
DOI : 10.1002/cpa.3160280206

M. D. Donsker and S. R. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time???III, Communications on Pure and Applied Mathematics, vol.19, issue.4, pp.389-461, 1976.
DOI : 10.1002/cpa.3160290405

M. D. Donsker and S. R. Varadhan, Asymptotic evaluation of certain markov process expectations for large time. IV, Communications on Pure and Applied Mathematics, vol.58, issue.2, pp.183-212, 1983.
DOI : 10.1002/cpa.3160360204

R. A. Blythe and M. R. Evans, Nonequilibrium steady sstates of matrix product form: A solver's guide J. Phys. A, pp.333-441, 2007.

M. Gorissen, A. Lazarescu, K. Mallick, and C. Vanderzande, Exact Current Statistics of the Asymmetric Simple Exclusion Process with Open Boundaries, Physical Review Letters, vol.109, issue.17, 2012.
DOI : 10.1103/PhysRevLett.109.170601

G. W. Paltridge, Global dynamics and climate - a system of minimum entropy exchange, Quarterly Journal of the Royal Meteorological Society, vol.19, issue.429, pp.475-484, 1975.
DOI : 10.1002/qj.49710142906

H. Ozawa, A. Ohmura, R. Lorenz, and T. Pujol, The second law of thermodynamics and the global climate system: A review of the maximum entropy production principle, Reviews of Geophysics, vol.45, issue.2, pp.4110-1029, 2003.
DOI : 10.1029/2002RG000113

C. Herbert, D. Paillard, M. Kageyama, and B. Dubrulle, Present and Last Glacial Maximum climates as states of maximum entropy production, Quarterly Journal of the Royal Meteorological Society, vol.45, issue.657, pp.1059-1069, 2011.
DOI : 10.1002/qj.832
URL : https://hal.archives-ouvertes.fr/cea-00917319

R. C. Dewar, Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states, Journal of Physics A: Mathematical and General, vol.36, issue.3, pp.631-641, 2003.
DOI : 10.1088/0305-4470/36/3/303

G. Grinstein and R. Linsker, Comments on a derivation and application of the ???maximum entropy production??? principle, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.31, pp.9717-9720, 2007.
DOI : 10.1088/1751-8113/40/31/N01

S. Bruers, A discussion on maximum entropy production and information theory, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.27, pp.7441-7450, 2007.
DOI : 10.1088/1751-8113/40/27/003

C. Monthus, Non-equilibrium steady states: maximization of the Shannon entropy associated with the distribution of dynamical trajectories in the presence of constraints, Journal of Statistical Mechanics: Theory and Experiment, vol.2011, issue.03, pp.10-1088, 2011.
DOI : 10.1088/1742-5468/2011/03/P03008

A. Parmeggiani, T. Franosch, and E. Frey, Phase Coexistence in Driven One-Dimensional Transport, Physical Review Letters, vol.90, issue.8, pp.90-086601, 2003.
DOI : 10.1103/PhysRevLett.90.086601

P. Billingsley, Ergodic Theory and Information, 1965.

V. Latora, M. Baranger, and A. Rapisarda, The rate of entropy increase at the edge of chaos, Physics Letters A, vol.273, issue.1-2, pp.97-103, 2000.
DOI : 10.1016/S0375-9601(00)00484-9

L. M. Martyushev and V. D. Seleznev, Maximum entropy production principle in physics, chemistry and biology, Physics Reports, vol.426, issue.1, pp.1-45, 2006.
DOI : 10.1016/j.physrep.2005.12.001

J. S. Kirkaldy, Entropy criteria applied to pattern selection in systems with free boundaries, Metallurgical Transactions A, vol.14, issue.10, pp.1781-1797, 1985.
DOI : 10.1007/BF02670366

V. Lecomte, C. Appert-rolland, and F. Van-wijland, Thermodynamic Formalism for Systems with Markov Dynamics, Journal of Statistical Physics, vol.102, issue.1, pp.51-106, 2007.
DOI : 10.1007/s10955-006-9254-0
URL : https://hal.archives-ouvertes.fr/hal-00107948