A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, Negative thermal conductivity of chains of rotors with mechanical forcing, Physical Review E, vol.84, issue.6, p.61108, 2011.
DOI : 10.1103/PhysRevE.84.061108

URL : https://hal.archives-ouvertes.fr/hal-00608036

J. Maillet, G. Vallverdu, N. Desbiens, and G. Stoltz, Molecular simulations of shock to detonation transition in nitromethane, Europhys. Lett, pp.96-68007, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00609415

R. Joubaud and G. Stoltz, Nonequilibrium shear viscosity computations with Langevin dynamics, Multiscale Model, pp.191-216, 2011.

N. Chopin, T. Lelì-evre, and G. Stoltz, Free energy methods for Bayesian inference: efficient exploration of univariate Gaussian mixture posteriors, Statistics and Computing, vol.86, issue.10, pp.897-916, 2012.
DOI : 10.1007/s11222-011-9257-9

URL : https://hal.archives-ouvertes.fr/hal-00460914

C. Bernardin and G. Stoltz, Anomalous diffusion for a class of systems with two conserved quantities, Nonlinearity, vol.25, issue.4, pp.1099-1133, 2012.
DOI : 10.1088/0951-7715/25/4/1099

URL : https://hal.archives-ouvertes.fr/ensl-00909792

T. Lelì-evre, M. Rousset, and G. Stoltz, Langevin dynamics with constraints and computation of free energy differences, to appear in Math, Comput, 2012.

E. Cancès, G. Stoltzs1, ]. M. Dobson, F. Legoll, T. Lelì-evre et al., A mathematical formulation of the random phase approximation for crystals, accepted in Ann. I. H. Poincare-An Derivation of Langevin ynamics in a non-zero background flow, p.680278, 2012.

C. Leimkuhler and G. Stoltz, Sampling techniques for computational statistical physics, Conference proceedings and general audience articles [ Encyclopedia of Applied and Computational Mathematics, 2012.

G. Stoltz, Calculation of ensemble averages, Encyclopedia of Applied and Computational Mathematics, 2012.

G. Stoltz, Computation of free energy differences, Encyclopedia of Applied and Computational Mathematics, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00495517

E. Cancès, M. Lewin, and G. Stoltz, The Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint, Lecture Notes in Computational Science and Engineering, vol.82, pp.87-125, 2011.
DOI : 10.1007/978-3-642-21943-6_5

F. Legoll, T. Lelì-evre, and G. Stoltz, Some remarks on sampling methods in Molecular Dynamics, Proceedings of CANUM 2006, pp.217-233, 2008.
DOI : 10.1051/proc:072226

.. Linear-response-for-nonequilibrium-dynamics, 34 3.1.3.1 Reference equilibrium dynamics 34 3.1.3.2 Invariant measure of the nonequilibrium dynamics 34 3.1.3.3 Linear response and correlation functions, Artificial dynamics, p.38

.. Mathematical-analysis-of-the-viscosity, 46 3.3.2.1 Local conservation of the longitudinal velocity 46 3.3.2.2 Closure relation and definition of the viscosity, p.48

.. Adiabatic-switching-of-non-degenerate-eigenstates, 56 4.1.2.1 Switching procedure, p.58

]. S. Adler, Quantum Theory of the Dielectric Constant in Real Solids, Physical Review, vol.126, issue.2, pp.413-420, 1962.
DOI : 10.1103/PhysRev.126.413

L. Ambrosio, A. Figalli, G. Friesecke, J. Giannoulis, and T. Paul, Semiclassical limit of quantum dynamics with rough potentials and well-posedness of transport equations with measure initial data, Communications on Pure and Applied Mathematics, vol.37, issue.3, pp.1199-1242, 2011.
DOI : 10.1002/cpa.20371

URL : https://hal.archives-ouvertes.fr/hal-00496369

L. Ambrosio, G. Friesecke, and J. Giannoulis, Passage from Quantum to Classical Molecular Dynamics in the Presence of Coulomb Interactions, Communications in Partial Differential Equations, vol.115, issue.8, pp.1490-1515, 2010.
DOI : 10.1098/rspa.1932.0165

L. Ambrosio, N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_2

A. Arnold, Self-consistent relaxation-time models in quantum mechanics, Communications in Partial Differential Equations, vol.68, issue.1991, pp.3-4, 1996.
DOI : 10.1080/03605309608821193

A. Arnold, P. A. Markowich, G. Toscani, and A. Unterreiter, ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS, Communications in Partial Differential Equations, vol.324, issue.1-2, pp.43-100, 2001.
DOI : 10.1007/s002200050631

F. Aryasetiawan and O. Gunnarsson, The GW method, Rep. Prog. Phys, vol.61, issue.237, 1998.

J. E. Avron, R. Seiler, and L. G. Yaffe, Adiabatic theorems and applications to the quantum hall effect, Communications in Mathematical Physics, vol.52, issue.1, pp.33-49, 1987.
DOI : 10.1007/BF01209015

D. Bakry and M. Emery, Diffusions hypercontractives, Diffusions hypercontractives Séminaire de Probabilités XIX, pp.177-206, 1985.
DOI : 10.1007/BFb0075847

R. Balian, From Microphysics to Macrophysics. Methods and Applications of Statistical Physics, volume I -II, 2007.

G. Basile, C. Bernardin, and S. Olla, Momentum Conserving Model with Anomalous Thermal Conductivity in Low Dimensional Systems, Physical Review Letters, vol.96, issue.20, p.96, 2006.
DOI : 10.1103/PhysRevLett.96.204303

G. Basile, C. Bernardin, and S. Olla, Thermal Conductivity for a Momentum Conservative Model, Communications in Mathematical Physics, vol.28, issue.1, pp.67-98, 2009.
DOI : 10.1007/s00220-008-0662-7

C. Bernardin and P. Gonçalves, Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions, arXiv preprint 1205, p.1879, 2012.

C. Bernardin and S. Olla, Nonequilibrium macroscopic dynamics of chains of anharmonic oscillators

C. Bernardin and S. Olla, Transport Properties of a Chain of Anharmonic Oscillators with Random Flip of Velocities, Journal of Statistical Physics, vol.126, issue.3???4, pp.1224-1255, 2011.
DOI : 10.1007/s10955-011-0385-6

URL : https://hal.archives-ouvertes.fr/ensl-00589672

C. Bloch and J. Horowitz, Sur la d??termination des premiers ??tats d'un syst??me de fermions dans le cas d??g??n??r??, Nuclear Physics, vol.8, pp.91-97, 1958.
DOI : 10.1016/0029-5582(58)90136-6

F. Bonetto, J. L. Lebowitz, and L. Rey-bellet, FOURIER'S LAW: A CHALLENGE TO THEORISTS, Mathematical Physics, pp.128-151, 2000.
DOI : 10.1142/9781848160224_0008

N. Bou-rabee and H. Owhadi, Long-Run Accuracy of Variational Integrators in the Stochastic Context, SIAM Journal on Numerical Analysis, vol.48, issue.1, pp.278-297, 2010.
DOI : 10.1137/090758842

. Ph, H. Briet, B. Cornean, and . Savoie, A rigorous proof of the Landau-Peierls formula and much more, pp.1-40, 2012.

E. Cancès, M. Defranceschi, W. Kutzelnigg, C. L. Bris, and Y. Maday, Computational quantum chemistry: A primer, In Handbook of Numerical Analysis (Special volume on computational chemistry, pp.3-270, 2003.

E. Cancès, A. Deleurence, and M. Lewin, A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case, Commun. Math. Phys, pp.281-129, 2008.

E. Cancès and M. Lewin, The Dielectric Permittivity of Crystals in the Reduced Hartree???Fock Approximation, Archive for Rational Mechanics and Analysis, vol.129, issue.1, pp.139-177, 2010.
DOI : 10.1007/s00205-009-0275-0

P. Carmona, Existence and uniqueness of an invariant measure for a chain of oscillators in contact with two heat baths, Stochastic Processes and their Applications, vol.117, issue.8, pp.1076-1092, 2007.
DOI : 10.1016/j.spa.2006.12.003

URL : https://hal.archives-ouvertes.fr/hal-00115627

E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Constrained reaction coordinate dynamics for the simulation of rare events, Chemical Physics Letters, vol.156, issue.5, pp.472-477, 1989.
DOI : 10.1016/S0009-2614(89)87314-2

A. Casher and J. L. Lebowitz, Heat Flow in Regular and Disordered Harmonic Chains, Journal of Mathematical Physics, vol.12, issue.8, pp.1701-1711, 1971.
DOI : 10.1063/1.1665794

I. Catto, C. L. Bris, and P. Lions, On the thermodynamic limit for??Hartree???Fock type models, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.18, issue.6, pp.687-760, 2001.
DOI : 10.1016/S0294-1449(00)00059-7

URL : https://hal.archives-ouvertes.fr/hal-00157679

C. W. Chang, D. Okawa, H. Garcia, A. Majumdar, and A. Zettl, Breakdown of Fourier???s Law in Nanotube Thermal Conductors, Physical Review Letters, vol.101, issue.7, p.75903, 2008.
DOI : 10.1103/PhysRevLett.101.075903

G. Ciccotti, T. Lelì, and E. Vanden-eijnden, Projection of diffusions on submanifolds: Application to mean force computation, Communications on Pure and Applied Mathematics, vol.123, issue.3, pp.371-408, 2008.
DOI : 10.1002/cpa.20210

G. E. Crooks, Nonequilibrium measurements of free energy-differences for microscopically reversible Markovian systems, Journal of Statistical Physics, vol.90, issue.5/6, pp.1481-1487, 1998.
DOI : 10.1023/A:1023208217925

G. E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Physical Review E, vol.60, issue.3, pp.2721-2726, 1999.
DOI : 10.1103/PhysRevE.60.2721

S. Cuccagna, Dispersion for Schrodinger Equation with Periodic Potential in 1D, Communications in Partial Differential Equations, vol.33, issue.11, pp.2064-2095, 2008.
DOI : 10.1080/03605300802501582

P. J. Daivis and B. D. Todd, A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows, The Journal of Chemical Physics, vol.124, issue.19, 2006.
DOI : 10.1063/1.2192775

E. Darve, Thermodynamic Integration Using Constrained and Unconstrained Dynamics, pp.119-170, 2007.
DOI : 10.1007/978-3-540-38448-9_4

E. Darve and A. Porohille, Calculating free energies using average force, The Journal of Chemical Physics, vol.115, issue.20, pp.9169-9183, 2001.
DOI : 10.1063/1.1410978

S. Datta, Quantum Transport: From Atom to Transistor, 2005.
DOI : 10.1017/CBO9781139164313

URL : http://cds.cern.ch/record/826119/files/0521631459_TOC.pdf

R. Dautray and J. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Evolution Problems I, 2000.

W. K. Otter, Thermodynamic integration of the free energy along a reaction coordinate in Cartesian coordinates, The Journal of Chemical Physics, vol.112, issue.17, pp.7283-7292, 2000.
DOI : 10.1063/1.481329

W. K. Otter and W. J. Briels, The calculation of free-energy differences by constrained molecular-dynamics simulations, The Journal of Chemical Physics, vol.109, issue.11, pp.4139-4146, 1998.
DOI : 10.1063/1.477019

B. Derrida, J. L. Lebowitz, and E. R. Speer, Large deviation of the density profile in the steady state of the open symmetric simple exclusion process, Journal of Statistical Physics, vol.107, issue.3/4, pp.599-634, 2002.
DOI : 10.1023/A:1014555927320

A. Dhar, Heat Conduction in the Disordered Harmonic Chain Revisited, Physical Review Letters, vol.86, issue.26, pp.5882-5885, 2001.
DOI : 10.1103/PhysRevLett.86.5882

A. Dhar, Heat transport in low-dimensional systems, Advances in Physics, vol.151, issue.5, pp.457-537, 2008.
DOI : 10.1103/PhysRevLett.95.104302

A. Dhar and J. L. Lebowitz, Effect of Phonon-Phonon Interactions on Localization, Physical Review Letters, vol.100, issue.13, 2008.
DOI : 10.1103/PhysRevLett.100.134301

S. Duane, A. D. Kennedy, B. J. Pendleton, D. Roweth, and H. Monte-carlo, Hybrid Monte Carlo, Physics Letters B, vol.195, issue.2, pp.216-222, 1987.
DOI : 10.1016/0370-2693(87)91197-X

W. E. and E. Vanden-eijnden, Metastability, conformation dynamics, and transition pathways in complex systems, In Multiscale Modelling and Simulation, Lect. Notes Comput. Sci. Eng, vol.39, pp.35-68, 2004.

J. Eckmann and M. Hairer, Non-Equilibrium Statistical Mechanics??of Strongly Anharmonic Chains of Oscillators, Communications in Mathematical Physics, vol.212, issue.1, pp.105-164, 2000.
DOI : 10.1007/s002200000216

J. Eckmann, C. Pillet, and L. Rey-bellet, Entropy production in nonlinear, thermally driven Hamiltonian systems, Journal of Statistical Physics, vol.95, issue.1/2, pp.305-331, 1999.
DOI : 10.1023/A:1004537730090

URL : https://hal.archives-ouvertes.fr/hal-00005455

J. Eckmann, C. Pillet, and L. Rey-bellet, Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures, Communications in Mathematical Physics, vol.201, issue.3, pp.657-697, 1999.
DOI : 10.1007/s002200050572

URL : https://hal.archives-ouvertes.fr/hal-00005454

H. Ehrenreich and M. H. Cohen, Self-Consistent Field Approach to the Many-Electron Problem, Physical Review, vol.115, issue.4, pp.786-790, 1959.
DOI : 10.1103/PhysRev.115.786

E. Engel and R. M. Dreizler, Density Functional Theory ? An advanced course, Theoretical and Mathematical Physics, 2011.

D. J. Evans, Homogeneous NEMD algorithm for thermal conductivity???Application of non-canonical linear response theory, Physics Letters A, vol.91, issue.9, pp.457-460, 1982.
DOI : 10.1016/0375-9601(82)90748-4

D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids, 2008.
DOI : 10.1017/CBO9780511535307

F. Zhang, D. J. Isbister, and D. J. Evans, Nonequilibrium molecular dynamics simulations of heat flow in one-dimensional lattices, Physical Review E, vol.61, issue.4, pp.3541-3546, 2000.
DOI : 10.1103/PhysRevE.61.3541

L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, 1992.

B. Farid, Ground and low-lying excited states of interacting electron systems: a survey and some critical analyses, In Electron Correlation in the Solid State, pp.103-261, 1999.

J. Fritz, T. Funaki, and J. L. Lebowitz, Stationary states of random Hamiltonian systems, Probability Theory and Related Fields, vol.22, issue.2, pp.211-236, 1994.
DOI : 10.1007/BF01199023

L. M. Garrido, Generalized Adiabatic Invariance, Journal of Mathematical Physics, vol.5, issue.3, pp.335-362, 1964.
DOI : 10.1063/1.1704127

M. Gell-mann and F. Low, Bound States in Quantum Field Theory, Physical Review, vol.84, issue.2, pp.350-354, 1951.
DOI : 10.1103/PhysRev.84.350

O. V. Gendelman and A. V. Savin, Normal Heat Conductivity of the One-Dimensional Lattice with Periodic Potential of Nearest-Neighbor Interaction, Physical Review Letters, vol.84, issue.11, pp.2381-2384, 2000.
DOI : 10.1103/PhysRevLett.84.2381

O. V. Gendelman and A. V. Savin, Gendelman and Savin Reply:, Physical Review Letters, vol.94, issue.21, p.219405, 2005.
DOI : 10.1103/PhysRevLett.94.219405

J. B. Goodman and K. K. Lin, Coupling control variates for Markov chain Monte Carlo, Journal of Computational Physics, vol.228, issue.19, pp.7127-7136, 2009.
DOI : 10.1016/j.jcp.2009.03.043

E. M. Gosling, I. R. Mcdonald, and K. Singer, On the calculation by molecular dynamics of the shear viscosity of a simple fluid, Molecular Physics, vol.17, issue.6, pp.26-1475, 1973.
DOI : 10.1103/PhysRevA.4.1616

L. Gross, Logarithmic Sobolev Inequalities, American Journal of Mathematics, vol.97, issue.4, pp.1061-1083, 1975.
DOI : 10.2307/2373688

M. J. Gruber, Positive measure spectrum for Schr??dinger operators with periodic magnetic fields, Journal of Mathematical Physics, vol.44, issue.4, pp.1584-1595, 2003.
DOI : 10.1063/1.1556551

A. Guionnet and B. Zegarlinski, Lectures on Logarithmic Sobolev Inequalities, Séminaire de Probabilités XXXVI, pp.1-134, 2003.
DOI : 10.1007/978-3-540-36107-7_1

G. A. Hagedorn, Adiabatic expansions near eigenvalue crossings, Annals of Physics, vol.196, issue.2, pp.278-295, 1989.
DOI : 10.1016/0003-4916(89)90179-6

G. A. Hagedorn and A. Joye, A Time-Dependent Born-Oppenheimer Approximation with Exponentially Small Error Estimates, Communications in Mathematical Physics, vol.223, issue.3, pp.583-626, 2001.
DOI : 10.1007/s002200100562

URL : https://hal.archives-ouvertes.fr/hal-01260634

G. A. Hagedorn and A. Joye, Mathematical analysis of Born-Oppenheimer approximations , In Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon's 60th birthday, Proc. Sympos. Pure Math. (Amer. Math. Soc, vol.76, pp.203-226, 2007.

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration: Structure- Preserving Algorithms for Ordinary Differential Equations, 2006.

M. Hairer and J. Mattingly, Slow energy dissipation in anharmonic oscillator chains, Communications on Pure and Applied Mathematics, vol.12, issue.1, pp.999-1032, 2009.
DOI : 10.1002/cpa.20280

M. Hairer and G. Pavliotis, Periodic Homogenization for Hypoelliptic Diffusions, Journal of Statistical Physics, vol.117, issue.1/2, pp.261-279, 2004.
DOI : 10.1023/B:JOSS.0000044055.59822.20

M. Hairer and G. Pavliotis, From Ballistic to Diffusive Behavior in Periodic Potentials, Journal of Statistical Physics, vol.58, issue.1, pp.175-202, 2008.
DOI : 10.1007/s10955-008-9493-3

C. Hartmann, An Ergodic Sampling Scheme for Constrained Hamiltonian Systems with Applications to Molecular Dynamics, Journal of Statistical Physics, vol.50, issue.7, pp.687-711, 2008.
DOI : 10.1007/s10955-007-9470-2

C. Hartmann and C. Schütte, A constrained hybrid Monte-Carlo algorithm and the problem of calculating the free energy in several variables, ZAMM, vol.5, issue.4, pp.700-710, 2005.
DOI : 10.1002/zamm.200410218

C. Hartmann and C. Schütte, A Geometric Approach to Constrained Molecular Dynamics and Free Energy, Communications in Mathematical Sciences, vol.3, issue.1, pp.1-20, 2005.
DOI : 10.4310/CMS.2005.v3.n1.a1

C. Hartmann and C. Schütte, Comment on two distinct notions of free energy, Physica D: Nonlinear Phenomena, vol.228, issue.1, pp.59-63, 2007.
DOI : 10.1016/j.physd.2007.02.006

W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.97-109, 1970.
DOI : 10.1093/biomet/57.1.97

T. Hatano, Heat conduction in the diatomic Toda lattice revisited, Physical Review E, vol.59, issue.1, pp.1-4, 1999.
DOI : 10.1103/PhysRevE.59.R1

L. Hedin, New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem, Physical Review, vol.139, issue.3A, pp.796-823, 1965.
DOI : 10.1103/PhysRev.139.A796

L. Hedin and S. Lundqvist, Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids, Solid State Physics, vol.23, pp.1-181, 1969.
DOI : 10.1016/S0081-1947(08)60615-3

P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Physical Review, vol.136, issue.3B, pp.864-871, 1964.
DOI : 10.1103/PhysRev.136.B864

R. Holley and D. Stroock, Logarithmic Sobolev inequalities and stochastic Ising models, Journal of Statistical Physics, vol.42, issue.5-6, pp.5-6, 1987.
DOI : 10.1007/BF01011161

A. M. Horowitz, A generalized guided Monte Carlo algorithm, Physics Letters B, vol.268, issue.2, pp.247-252, 1991.
DOI : 10.1016/0370-2693(91)90812-5

R. J. Hulse, R. L. Howley, and W. V. Wilding, Transient Nonequilibrium Molecular Dynamic Simulations of Thermal Conductivity: 1. Simple Fluids, International Journal of Thermophysics, vol.12, issue.1, pp.1-12, 2005.
DOI : 10.1007/s10765-005-2349-z

M. Iannuzzi, A. Laio, and M. Parrinello, Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics, Physical Review Letters, vol.90, issue.23, p.238302, 2003.
DOI : 10.1103/PhysRevLett.90.238302

J. H. Irving and J. G. Kirkwood, The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics, The Journal of Chemical Physics, vol.18, issue.6, pp.817-829, 1950.
DOI : 10.1063/1.1747782

C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Physical Review E, vol.56, issue.5, pp.5018-5035, 1997.
DOI : 10.1103/PhysRevE.56.5018

C. Jarzynski, Nonequilibrium Equality for Free Energy Differences, Physical Review Letters, vol.78, issue.14, pp.2690-2693, 1997.
DOI : 10.1103/PhysRevLett.78.2690

T. Kato, On the Adiabatic Theorem of Quantum Mechanics, Journal of the Physical Society of Japan, vol.5, issue.6, pp.435-439, 1950.
DOI : 10.1143/JPSJ.5.435

T. Kato, Perturbation Theory for Linear Operators, Grundlehren der mathematischen Wissenschaften, vol.132, 1976.

C. Kipnis and C. Landim, Scaling limits of interacting particle systems, 1999.
DOI : 10.1007/978-3-662-03752-2

J. G. Kirkwood, Statistical Mechanics of Fluid Mixtures, The Journal of Chemical Physics, vol.3, issue.5, pp.300-313, 1935.
DOI : 10.1063/1.1749657

F. Klopp, Absolute continuity of the spectrum of a Landau Hamiltonian perturbed by a generic periodic potential, Mathematische Annalen, vol.137, issue.1, pp.675-687, 2010.
DOI : 10.1007/s00208-009-0452-3

URL : https://hal.archives-ouvertes.fr/hal-00376643

W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Physical Review, vol.140, issue.4A, pp.1133-1138, 1965.
DOI : 10.1103/PhysRev.140.A1133

A. Kundu, A. Dhar, and O. Narayan, The Green???Kubo formula for heat conduction in open systems, Journal of Statistical Mechanics: Theory and Experiment, vol.2009, issue.03, p.3001, 2009.
DOI : 10.1088/1742-5468/2009/03/L03001

J. Latorre, C. Hartmann, and C. , Schütte, Free energy computation by controlled Langevin processes, Procedia Computer Science, vol.1, pp.1591-1600, 2010.
DOI : 10.1016/j.procs.2010.04.179

URL : http://doi.org/10.1016/j.procs.2010.04.179

A. W. Lees and S. F. Edwards, The computer study of transport processes under extreme conditions, Journal of Physics C: Solid State Physics, vol.5, issue.15, 1921.
DOI : 10.1088/0022-3719/5/15/006

R. Lefevere, On the local space???time structure of non-equilibrium steady states, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.01, p.1004, 2007.
DOI : 10.1088/1742-5468/2007/01/P01004

URL : https://hal.archives-ouvertes.fr/hal-00130154

V. Legat, T. Lelì, and G. Samaey, A numerical closure approach for kinetic models of polymeric fluids: exploring closure relations for FENE dumbbells, Computers and Fluids, vol.43, pp.119-133, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00654570

B. J. Leimkuhler and S. Reich, Simulating Hamiltonian Dynamics, Cambridge Monographs on Applied and Computational Mathematics, vol.14, 2005.
DOI : 10.1017/CBO9780511614118

URL : https://repozitorij.uni-lj.si/Dokument.php?id=39532

B. J. Leimkuhler and R. D. Skeel, Symplectic Numerical Integrators in Constrained Hamiltonian Systems, Journal of Computational Physics, vol.112, issue.1, pp.117-125, 1994.
DOI : 10.1006/jcph.1994.1085

S. Lepri, R. Livi, and A. Politi, Thermal conduction in classical low-dimensional lattices, Physics Reports, vol.377, issue.1, pp.1-80, 2003.
DOI : 10.1016/S0370-1573(02)00558-6

E. H. Lieb, Density functionals for coulomb systems, International Journal of Quantum Chemistry, vol.140, issue.3, pp.243-277, 1983.
DOI : 10.1002/qua.560240302

P. B. Mackenzie, An improved hybrid Monte Carlo method, Physics Letters B, vol.226, issue.3-4, pp.369-371, 1989.
DOI : 10.1016/0370-2693(89)91212-4

A. Maeda and T. Munakata, Lattice thermal conductivity via homogeneous nonequilibrium molecular dynamics, Physical Review E, vol.52, issue.1, pp.234-239, 1995.
DOI : 10.1103/PhysRevE.52.234

J. Maillet, M. Mareschal, L. Soulard, R. Ravelo, P. S. Lomdahl et al., Uniaxial Hugoniostat:???A method for atomistic simulations of shocked materials, Physical Review E, vol.63, issue.1, p.16121, 2000.
DOI : 10.1103/PhysRevE.63.016121

S. Marsili, A. Barducci, R. Chelli, P. Procacci, and V. Schettino, Self-healing Umbrella Sampling:?? A Non-equilibrium Approach for Quantitative Free Energy Calculations, The Journal of Physical Chemistry B, vol.110, issue.29, pp.14011-14013, 2006.
DOI : 10.1021/jp062755j

A. Martinez and V. Sordoni, A general reduction scheme for the time-dependent Born???Oppenheimer approximation, Comptes Rendus Mathematique, vol.334, issue.3, pp.185-188, 2002.
DOI : 10.1016/S1631-073X(02)02212-4

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1091, 1953.
DOI : 10.1063/1.1699114

G. Nenciu, On the adiabatic theorem of quantum mechanics, Journal of Physics A: Mathematical and General, vol.13, issue.2, pp.15-18, 1980.
DOI : 10.1088/0305-4470/13/2/002

G. Nenciu and G. Rasche, Adiabatic theorem and Gell-Mann & Low formula, Helvetica Physica Acta, vol.62, pp.372-388, 1989.

S. Olla, Energy Diffusion and Superdiffusion in??Oscillators Lattice Networks, In New Trends in Mathematical Physics, pp.539-547, 2009.
DOI : 10.1007/978-90-481-2810-5_36

URL : https://hal.archives-ouvertes.fr/hal-00319532

M. Ottobre and G. A. Pavliotis, Asymptotic analysis for the generalized Langevin equation, Nonlinearity, vol.24, issue.5, pp.1629-1653, 2010.
DOI : 10.1088/0951-7715/24/5/013

G. Panati, H. Spohn, and S. Teufel, Space-adiabatic perturbation theory, Advances in Theoretical and Mathematical Physics, vol.7, issue.1, pp.145-204, 2003.
DOI : 10.4310/ATMP.2003.v7.n1.a6

G. Papanicolaou and S. R. Varadhan, Ornstein-Uhlenbeck process in a random potential, Commun. Math. Phys, vol.38, issue.06, pp.819-834, 1985.

G. A. Pavliotis and A. M. Stuart, Periodic homogenization for inertial particles, Physica D: Nonlinear Phenomena, vol.204, issue.3-4, pp.161-187, 2005.
DOI : 10.1016/j.physd.2005.04.011

URL : http://arxiv.org/abs/cond-mat/0504405

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, vol.44, 1983.
DOI : 10.1007/978-1-4612-5561-1

D. C. Rapaport, The Art of Molecular Dynamics Simulations, 1995.

M. Reed and B. Simon, Methods of Modern Mathematical Physics. Fourier Analysis and Self-adjointness, volume II, 1975.

M. Reed and B. Simon, Methods of Modern Mathematical Physics, Analysis of Operators, vol.IV, 1978.

M. Reed and B. Simon, Methods of Modern Mathematical Physics. Scattering Theory, volume III, 1979.

P. Reimann, Brownian motors: noisy transport far from equilibrium, Physics Reports, vol.361, issue.2-4, pp.57-265, 2002.
DOI : 10.1016/S0370-1573(01)00081-3

URL : http://arxiv.org/abs/cond-mat/0010237

L. Rey-bellet, Ergodic Properties of Markov Processes, Open Quantum Systems II, pp.1-39, 2006.
DOI : 10.1007/3-540-33966-3_1

L. Rey-bellet, Open Classical Systems, In Open Quantum Systems II Lecture Notes in Mathematics, vol.1881, pp.41-78, 2006.
DOI : 10.1007/3-540-33966-3_2

L. Rey-bellet and L. E. Thomas, Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics, Communications in Mathematical Physics, vol.225, issue.2, pp.305-329, 2002.
DOI : 10.1007/s002200100583

L. Rey-bellet and L. E. Thomas, Fluctuations of the Entropy Production in Anharmonic Chains, Annales Henri Poincar??, vol.3, issue.3, pp.483-502, 2002.
DOI : 10.1007/s00023-002-8625-6

Z. Rieder, J. L. Lebowitz, and E. Lieb, Properties of a Harmonic Crystal in a Stationary Nonequilibrium State, Journal of Mathematical Physics, vol.8, issue.5, pp.1073-1078, 1967.
DOI : 10.1063/1.1705319

H. Rodenhausen, Einstein's relation between diffusion constant and mobility for a diffusion model, Journal of Statistical Physics, vol.38, issue.5-6, pp.1065-1088, 1989.
DOI : 10.1007/BF01041079

R. J. Rubin and W. L. Greer, Abnormal Lattice Thermal Conductivity of a One???Dimensional, Harmonic, Isotopically Disordered Crystal, Journal of Mathematical Physics, vol.12, issue.8, pp.1686-1701, 1971.
DOI : 10.1063/1.1665793

S. S. Sarman, D. J. Evans, and P. T. Cummings, Recent developments in non-Newtonian molecular dynamics, Physics Reports, vol.305, issue.1-2, pp.1-92, 1998.
DOI : 10.1016/S0370-1573(98)00018-0

J. Schlitter and M. Klähn, A new concise expression for the free energy of a reaction coordinate, The Journal of Chemical Physics, vol.118, issue.5, pp.2057-2060, 2003.
DOI : 10.1063/1.1534578

H. Schulz-baldes and S. Teufel, Orbital polarization and magnetization for independent particles in disordered media, arXiv preprint 1201, p.4812, 2012.

M. R. Shirts and J. D. Chodera, Statistically optimal analysis of samples from multiple equilibrium states, The Journal of Chemical Physics, vol.129, issue.12, p.124105, 2008.
DOI : 10.1063/1.2978177

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2671659

B. Simon, Trace Ideals and Their Applications, 1979.
DOI : 10.1090/surv/120

J. Sjöstrand, Projecteurs adiabatiques du point de vue pseudodifférentiel, C. R. Acad. Sci. Paris Sér. I Math, vol.317, issue.2, pp.217-220, 1993.

J. Solovej, Proof of the ionization conjecture in a reduced Hartree-Fock model, Inventiones mathematicae, vol.79, issue.1, pp.291-311, 1991.
DOI : 10.1007/BF01245077

M. Sprik and G. Ciccoti, Free energy from constrained molecular dynamics, The Journal of Chemical Physics, vol.109, issue.18, pp.7737-7744, 1998.
DOI : 10.1063/1.477419

G. Stoltz, Some mathematical methods for molecular and multiscale simulation, 2007.
URL : https://hal.archives-ouvertes.fr/tel-00166728

S. Teufel, Adiabatic perturbation theory in quantum dynamics, Lecture Notes in Mathematics, vol.1821, 2003.
DOI : 10.1007/b13355

L. E. Thomas, Time dependent approach to scattering from impurities in a crystal, Communications in Mathematical Physics, vol.69, issue.4, pp.335-343, 1973.
DOI : 10.1007/BF01646745

M. Toda, Solitons and Heat Conduction, Physica Scripta, vol.20, issue.3-4, pp.424-430, 1979.
DOI : 10.1088/0031-8949/20/3-4/017

B. D. Todd and P. J. Daivis, Homogeneous non-equilibrium molecular dynamics simulations of viscous flow: techniques and applications, Molecular Simulation, vol.67, issue.3, pp.189-229, 2007.
DOI : 10.1016/S1359-0294(98)80088-5

B. D. Todd, D. J. Evans, and P. J. Daivis, Pressure tensor for inhomogeneous fluids, Physical Review E, vol.52, issue.2, pp.1627-1638, 1995.
DOI : 10.1103/PhysRevE.52.1627

E. Vanden-eijnden and G. Ciccotti, Second-order integrators for Langevin equations with holonomic constraints, Chemical Physics Letters, vol.429, issue.1-3, pp.310-316, 2006.
DOI : 10.1016/j.cplett.2006.07.086

F. Wang and D. P. Landau, Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram, Physical Review E, vol.64, issue.5, p.56101, 2001.
DOI : 10.1103/PhysRevE.64.056101

F. G. Wang and D. P. Landau, Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States, Physical Review Letters, vol.86, issue.10, pp.2050-2053, 2001.
DOI : 10.1103/PhysRevLett.86.2050

Z. L. Wang, D. W. Tang, X. H. Zheng, W. G. Zhang, and Y. T. Zhu, Length-dependent thermal conductivity of single-wall carbon nanotubes: prediction and measurements, Nanotechnology, vol.18, issue.47, p.475714, 2007.
DOI : 10.1088/0957-4484/18/47/475714

N. Wiser, Dielectric Constant with Local Field Effects Included, Physical Review, vol.129, issue.1, pp.62-69, 1963.
DOI : 10.1103/PhysRev.129.62

L. Yang and B. Hu, Comment on ???Normal Heat Conductivity of the One-Dimensional Lattice with Periodic Potential of Nearest-Neighbor Interaction???, Physical Review Letters, vol.94, issue.21, p.219404, 2005.
DOI : 10.1103/PhysRevLett.94.219404

H. T. Yau, Relative entropy and hydrodynamics of Ginzburg-Landau models, Letters in Mathematical Physics, vol.77, issue.1, pp.63-80, 1991.
DOI : 10.1007/BF00400379

G. M. Zhislin and A. G. Sigalov, The spectrum of the energy operator for atoms with fixed nuclei on subspaces corresponding to irreducible representations of the group of permutations, Izv. Akad. Nauk SSSR Ser. Mat, pp.29-835, 1965.

X. Zotos, Ballistic transport in classical and quantum integrable systems, Journal of Low Temperature Physics, vol.126, issue.3/4, pp.1185-1194, 2002.
DOI : 10.1023/A:1013827615835

R. W. Zwanzig, High???Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases, The Journal of Chemical Physics, vol.22, issue.8, pp.1420-1426, 1954.
DOI : 10.1063/1.1740409