. I. Bibliography-[-akn07-]-v, V. V. Arnold, A. I. Kozlov, and . Neishtadt, Mathematical aspects of classical and celestial mechanics, 2007.

A. [. Avalos and . Mackie, Dissipative particle dynamics with energy conservation, Europhysics Letters (EPL), vol.40, issue.2, pp.141-146, 1997.
DOI : 10.1209/epl/i1997-00436-6

]. L. Arn74 and . Arnold, Stochastic Differential Equations, 1974.

F. [. Afshar, A. Schmid, S. Pishevar, and . Worley, Exploiting seeding of random number generators for efficient domain decomposition parallelization of dissipative particle dynamics, Computer Physics Communications, vol.184, issue.4, pp.1119-1128, 2013.
DOI : 10.1016/j.cpc.2012.12.003

T. [. Alder and . Wainwright, Molecular dynamics by electronic computers, Tran. Pr. Stat. Mech, pp.97-131, 1958.

G. [. Butler, O. G. Ayton, D. J. Jepps, and . Evans, Configurational temperature: Verification of Monte Carlo simulations, The Journal of Chemical Physics, vol.109, issue.16, pp.6519-6522, 1998.
DOI : 10.1063/1.477301

[. Baker, Alternants and continuous groups. P. Lond, Math. Soc, vol.2, issue.1, pp.24-47, 1905.
DOI : 10.1112/plms/s2-3.1.24

URL : http://plms.oxfordjournals.org/cgi/content/short/s2-3/1/24

A. Bruenger, C. L. Brooks, I. , and M. Karplus, Stochastic boundary conditions for molecular dynamics simulations of ST2 water, Chemical Physics Letters, vol.105, issue.5, pp.495-500, 1984.
DOI : 10.1016/0009-2614(84)80098-6

D. [. Balian, J. F. Haar, and . Gregg, From Microphysics to Macrophysics. Methods and Applications of Statistical Physics. Number vol. I in Theoretical and Mathematical Physics, 2006.
DOI : 10.1007/978-3-540-45475-5

. Bo-]-c, S. Bernardin, and . Olla, Thermodynamics and non-equilibrium macroscopic dynamics of chains of anharmonic oscillators

]. D. Bre90 and . Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Phys. Rev. B, vol.42, pp.9458-9471, 1990.

H. [. Bou-rabee and . 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

I. [. Besold, M. Vattulainen, J. M. Karttunen, . E. Polsoncam97-]-j, and . Campbell, Towards better integrators for dissipative particle dynamics simulations, Physical Review E, vol.62, issue.6, pp.7611-761414, 1897.
DOI : 10.1103/PhysRevE.62.R7611

URL : http://arxiv.org/abs/cond-mat/0010219

E. Cances, M. Defranceschi, W. Kutzelnigg, C. L. Bris, and Y. Maday, Computational quantum chemistry: a primer of Handbook of numerical analysis, Special VolumeCie15] E. Cieren. Molecular Dynamics for Exascale Supercomputers, pp.3-270, 2003.

M. [. Daw and . Baskes, Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals, Physical Review Letters, vol.50, issue.17, pp.1285-1288, 1983.
DOI : 10.1103/PhysRevLett.50.1285

M. [. Daw and . Baskes, Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals, Physical Review B, vol.29, issue.12, pp.6443-6453, 1984.
DOI : 10.1103/PhysRevB.29.6443

]. J. Dor96 and . Dormand, Numerical methods for differential equations: a computational approach, 1996.

. E. Dos-+-07-]-d, V. Discher, G. Ortiz, M. L. Srinivas, Y. Klein et al., Emerging applications of polymersomes in delivery: From molecular dynamics to shrinkage of tumors, Prog. in Polym. Sci, vol.32, pp.8-9838, 2007.

]. Eiy10 and . Eiyad, Natural Convection Heat Transfer Simulation using Energy Conservative Dissipative Particle Dynamics, Phys. Rev. E, vol.81, p.56704, 2010.

]. Eiy11 and . Eiyad, Application of Dissipative Particle Dynamics to Natural Convection in Differentially Heated Enclosures, Mol. Simulat, vol.37, issue.2, pp.135-152, 2011.

M. [. Español and . Revenga, Smoothed dissipative particle dynamics, Physical Review E, vol.67, issue.2, p.26705, 2003.
DOI : 10.1103/PhysRevE.67.026705

]. P. Esp97 and . Español, Dissipative Particle Dynamics with Energy Conservation, Europhys. Lett, vol.40, issue.6, pp.631-637, 1997.

P. Español and P. Warren, Statistical Mechanics of Dissipative Particle Dynamics, Europhysics Letters (EPL), vol.30, issue.4, p.191, 1995.
DOI : 10.1209/0295-5075/30/4/001

M. [. Foiles, M. S. Baskes, and . Daw, Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Physical Review B, vol.33, issue.12, pp.7983-7991, 1986.
DOI : 10.1103/PhysRevB.33.7983

]. M. Fis64 and . Fisher, The free energy of a macroscopic system, Arch. Ration. Mech. An, vol.17, issue.5, pp.377-410, 1964.

P. [. Goujon, D. J. Malfreyt, and . Tildesley, Mesoscopic simulation of entanglements using dissipative particle dynamics: Application to polymer brushes, The Journal of Chemical Physics, vol.129, issue.3, p.34902, 2008.
DOI : 10.1063/1.2954022

URL : https://hal.archives-ouvertes.fr/hal-00315981

A. [. Gikhman and . Skorokhod, Stochastic Differential Equations, 1972.
DOI : 10.1007/978-3-540-49941-1_2

P. [. Groot and . Warren, Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation, The Journal of Chemical Physics, vol.107, issue.11, pp.4423-4435, 1997.
DOI : 10.1063/1.474784

]. W. Has70, ]. Hastingshau06, and . Hausdorff, Monte-Carlo Samplings Methods using Markov Chains and their Applications Die symbolische exponentialformel in der gruppentheorie, Biometrika Ber. Verh. Kgl. Sächs. Ges. Wiss. Leipzig., Math.-phys. Kl, vol.57, issue.58, pp.97-116, 1906.

J. [. Hoogerbrugge and . Koelman, Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics, Europhysics Letters (EPL), vol.19, issue.3
DOI : 10.1209/0295-5075/19/3/001

H. E. Hairer, C. Lubich, and G. Wanner, Geometrical Numerical Integration - Structure-Preserving Algorithms for Ordinary Differential Equations, Europhys. Lett, vol.19, issue.31, p.155, 1992.

J. [. Hairer and . Mattingly, Yet Another Look at Harris' Ergodic Theorem for Markov Chains Random Fields and Applications VI, Seminar on Stochastic AnalysisJon24] J. E. Jones. On the Determination of Molecular Fields. II. From the Equation of State of a Gas. Roy. Soc. Lond. Proc. S. A, pp.109-117463, 1924.

]. W. Kli87 and . Kliemann, Recurrence and Invariant Measures for Degenerate Diffusions, Ann. Probab, vol.15, issue.2, pp.690-707, 1987.

]. M. Kop15a and . Kopec, Weak backward error analysis for langevin process Weak backward error analysis for overdamped langevin processes, BIT Num. Math. IMA J. Numer. Anal, vol.55, issue.352, pp.1057-1103583, 2015.

E. [. Kloeden and . Platen, Numerical Solution of Stochastic Differential Equations. Stochastic Modelling and Applied Probability, 2013.

]. P. Lan08 and . Langevin, Sur la théorie du Mouvement Brownien [On the theory of Brownian Motion], C. R. Acad. Sci. (Paris), vol.146, pp.530-533, 1908.

M. Lisal, J. K. Brennan, and J. B. Avalos, Dissipative particle dynamics at isothermal, isobaric, isoenergetic, and isoenthalpic conditions using Shardlow-like splitting algorithms, The Journal of Chemical Physics, vol.135, issue.20, p.135, 2011.
DOI : 10.1063/1.3660209

M. Moore, W. D. Lisal, and . Mattson, Parallel implementation of isothermal and isoenergetic dissipative particle dynamics using shardlow-like splitting algorithms, Comput. Phys. Commun, vol.185, issue.7, pp.1987-1998, 2014.

A. [. Lemons and . Gythiel, Paul Langevin's 1908 paper "on the theory of Brownian Motion" ["sur la théorie du Mouvement Brownien, C. R. Acad. Sci. (paris) Am. J. Phy, vol.146, issue.11, pp.530-533, 1908.

E. [. Landau and . Lifshitz, Statistical Physics, part I, 1980.

B. Leimkuhler, C. Matthews, G. Stoltz-leimkuhler, and S. Reich, The Computation of Averages from Equilibrium and Non-Equilibrium Langevin Molecular Dynamics Simulating Hamiltonian Dynamics, Stoltz. Free Energy Computation : A Mathematical Perspective, 2004.

X. [. Leimkuhler and . Shang, On the numerical treatment of dissipative particle dynamics and related systems, Journal of Computational Physics, vol.280, pp.72-95, 2015.
DOI : 10.1016/j.jcp.2014.09.008

G. [. Lelièvre and . Stoltz, Partial differential equations and stochastic methods in molecular dynamics, Acta Numerica, vol.24, pp.1-186, 2016.
DOI : 10.1063/1.2996509

B. [. Mackie, V. Avalos, and . Navas, Dissipative particle dynamics with energy conservation: Modelling of heat flow, Physical Chemistry Chemical Physics, vol.1, issue.9, pp.2039-2049, 1999.
DOI : 10.1039/a809502g

]. G. Mil86, Mil'shtein. Weak approximation of solutions of systems of stochastic differential equations, Theor. Proba. & Appl, vol.30, issue.4, pp.750-766, 1986.

T. [. Moeendarbary, M. Ng, and . Zangeneh, DISSIPATIVE PARTICLE DYNAMICS: INTRODUCTION, METHODOLOGY AND COMPLEX FLUID APPLICATIONS ??? A REVIEW, International Journal of Applied Mechanics, vol.01, issue.04, pp.1737-763, 2009.
DOI : 10.1142/S1758825109000381

H. Mori, Transport, Collective Motion, and Brownian Motion, Progress of Theoretical Physics, vol.33, issue.3, pp.423-455, 1965.
DOI : 10.1143/PTP.33.423

URL : http://ptp.oxfordjournals.org/cgi/content/short/33/3/423

A. [. Mattingly, D. J. Stuart, and . Higham, Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise, Stochastic Processes and their Applications, vol.101, issue.2, pp.185-232, 2002.
DOI : 10.1016/S0304-4149(02)00150-3

URL : http://doi.org/10.1016/s0304-4149(02)00150-3

J. B. Maillet, L. Soulard, and G. Stoltz, A reduced model for shock and detonation waves. II. The reactive case, Europhysics Letters (EPL), vol.78, issue.6, p.68001, 2007.
DOI : 10.1209/0295-5075/78/68001

URL : https://hal.archives-ouvertes.fr/hal-00125537

R. [. Meyn and . Tweedie, Markov Chains and Stochastic Stability. Communications and control engineering series, 1993.
DOI : 10.1007/978-1-4471-3267-7

M. [. Milstein and . Tretyakov, Stochastic Numerics for Mathematical Physics, 2004.
DOI : 10.1007/978-3-662-10063-9

[. Maillet, G. Vallverdu, N. Desbiens, and G. Stoltz, Mesoscopic simulations of shock-to-detonation transition in reactive liquid high explosive, EPL (Europhysics Letters), vol.96, issue.6, p.68007, 2011.
DOI : 10.1209/0295-5075/96/68007

URL : https://hal.archives-ouvertes.fr/hal-00676470

O. Durand and L. Soulard, Large- Scale Molecular Dynamic Study of Jet Break-up and Ejecta Production from Shock-Loaded Copper with a Hybrid Method, Feb 2012. [PHF98] I. Pagonabarraga, M. H. J. Hagen, and D. Frenkel. Self-Consistent Dissipative Particle Dynamics Algorithm, pp.377-382, 1998.

C. [. Root, T. Landis, and . Cleveland, Valence bond concepts applied to the molecular mechanics description of molecular shapes. 1. Application to nonhypervalent molecules of the P-block, Journal of the American Chemical Society, vol.115, issue.10, pp.4201-4209, 1993.
DOI : 10.1021/ja00063a043

]. D. Rue69 and . Ruelle, Statistical Physics: Rigourous Results, 1969.

M. Serrano, G. De-fabritiis, P. Español, and P. V. Coveney, A stochastic Trotter integration scheme for dissipative particle dynamics, Mathematics and Computers in Simulation, vol.72, issue.2-6, pp.190-194, 2006.
DOI : 10.1016/j.matcom.2006.05.019

]. T. Sha03 and . Shardlow, Splitting for Dissipative Particle Dynamics, SIAM J. Sci. Comput, vol.24, issue.4, pp.1267-1282, 2003.

]. G. Sto06 and . Stoltz, A Reduced Model for Shock and Detonation Waves. Part I. The Inert Case, Europhys. Lett, vol.77, issue.8, pp.849-855, 2006.

]. G. Str68 and . Strang, On the Construction and Comparison of Difference Schemes

Y. [. Shardlow and . Yan, GEOMETRIC ERGODICITY FOR DISSIPATIVE PARTICLE DYNAMICS, Stochastics and Dynamics, vol.06, issue.01, 2006.
DOI : 10.1142/S0219493706001670

]. D. Tal02 and . Talay, Stochastic hamiltonian systems: exponential convergence to the invariant measure, and discretization by the implicit euler scheme, Markov Processes Related Fields, pp.163-198, 2002.

]. H. Tro59 and . Trotter, On the Product of Semi-Groups of Operators

L. [. Talay and . Tubaro, Expansion of the global error for numerical schemes solving stochastic differential equations, Proc. Am, pp.545-551483, 1959.
DOI : 10.1080/07362999008809220

URL : https://hal.archives-ouvertes.fr/inria-00075490

]. M. Tuc10 and . Tuckerman, Statistical Mechanics: Theory and Molecular Simulation . Oxford Graduate Texts, 2010.

]. A. Van-duin, S. Dasgupta, F. Lorant, and I. W. Goddard, ReaxFF:?? A Reactive Force Field for Hydrocarbons, The Journal of Physical Chemistry A, vol.105, issue.41, pp.9396-9409, 2001.
DOI : 10.1021/jp004368u

]. L. Ver67 and . Verlet, Computer "experiments" on classical fluids. i. thermodynamical properties of lennard-jones molecules, Phys. Rev, vol.159, pp.98-103, 1967.

M. [. Vattulainen, G. Karttunen, J. M. Besold, and . Polson, Integration schemes for dissipative particle dynamics simulations: From softly interacting systems towards hybrid models, The Journal of Chemical Physics, vol.116, issue.10, pp.3967-3979, 2002.
DOI : 10.1063/1.1450554

URL : http://arxiv.org/abs/cond-mat/0211332

R. [. Wilhelm and . Battino, Estimation of Lennard???Jones (6,12) Pair Potential Parameters from Gas Solubility Data, The Journal of Chemical Physics, vol.55, issue.8, pp.4012-4017, 1971.
DOI : 10.1063/1.1676694

]. R. Zwa73 and . Zwanzig, Nonlinear generalized langevin equations, J. Stat. Phys, vol.9, issue.3, pp.215-220, 1973.