Free Energy Computations: A Mathematical Perspective

Together with Tony Lelièvre (CERMICS) and Mathias Rousset (INRIA Lille), we published a book on the mathematical study of free energy computations. See the book’s website at Imperial College Press. You can also find here the codes advertised in the preface to the book.

Molecular dynamics

  • T. Lelièvre, M. Rousset and G. Stoltz, Hybrid Monte Carlo methods for sampling probability measures on submanifolds, arXiv preprint 1807.02356 (2018) pdf
  • J. Roussel and G. Stoltz, A perturbative approach to control variates in molecular dynamics, arXiv preprint 1712.08022 (2017) pdf
  • G. Ferré and G. Stoltz, Error estimates on ergodic properties of discretized Feynman-Kac semigroups, arXiv preprint 1712.04013 (2017) pdf
  • G. Stoltz and E. Vanden-Eijnden, Longtime convergence of the Temperature-Accelerated Molecular Dynamics Method, Nonlinearity 31(8), 3748-3769 (2018) pdf
  • J. Roussel and G. Stoltz, Spectral methods for Langevin dynamics and associated error estimates, accepted for publication in M2AN (2017) pdf
  • A. Iacobucci, S. Olla and G. Stoltz, Convergence rates for nonequilibrium Langevin dynamics, accepted for publication in Ann. Math. Quebec (2017) pdf
  • G. Fort, B. Jourdain, T. Lelievre and G. Stoltz, Convergence and efficiency of adaptive importance sampling techniques with partial biasing, J. Stat. Phys. 171(2), 220-268 (2018) link
  • A. Lesage, T. Lelièvre, G. Stoltz and J. Hénin, Smoothed biasing forces yield unbiased free energies with the extended-system adaptive biasing force method, J. Phys. Chem. B 121(15), 3676–3685 (2017)
  • G. Stoltz and Z. Trstanova, Stable and accurate schemes for Langevin dynamics with general kinetic energies, Multiscale Model. Simul., 16(2), 777-806 (2018) preprint
  • T. Lelièvre and G. Stoltz, Partial differential equations and stochastic methods in molecular dynamics, Acta Numerica 25, 681-880 (2016) link
  • S. Redon, G. Stoltz and Z. Trstanova, Error Analysis of Modified Langevin Dynamics, J. Stat. Phys. 164(4), 735-771 (2016) preprint
  • I. G. Tejada, L. Brochard, T. Lelièvre, G. Stoltz, F. Legoll and E. Cancès, Coupling a reactive potential with a harmonic approximation for atomistic simulations of material failure, Computer Methods in Applied Mechanics and Engineering 305, 422-440 (2016) preprint
  • M. Fathi and G. Stoltz, Improving dynamical properties of stabilized discretizations of overdamped Langevin dynamics, Numer. Mathematik 136(2), 545–602 (2017) preprint
  • H. Spohn and G. Stoltz, Nonlinear fluctuating hydrodynamics in one dimension: the case of two conserved fields, J. Stat. Phys. 160(4), 861-884 (2015) preprint
  • G. Fort, B. Jourdain, T. Lelievre and G. Stoltz, Self-Healing Umbrella Sampling: Convergence and efficiency, Stat. Comput. 27(1) 147-168 (2017) preprint
  • R. Joubaud, G. Pavliotis and G. Stoltz, Langevin dynamics with space-time periodic nonequilibrium forcing, J. Stat. Phys. 158(1), 1-36 (2015) preprint
  • M. Fathi, A.-A. Homman and G. Stoltz, Error analysis of the transport properties of Metropolized schemes, ESAIM Proc. 48, 341-363 (2015) preprint
  • G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre and G. Stoltz, Efficiency of the Wang-Landau algorithm: a simple test case, Appl. Math. Res. Express 2014(2), 275-311 (2014) preprint
  • L. Cao, M.-C. Marinica, G. Stoltz, T. Lelièvre and M. Athènes, Using Bayes formula to average the biasing forces and recover free energies in adaptive Monte Carlo simulations, J. Chem. Phys. 140, 104108 (2014) pdf
  • B. Leimkuhler, Ch. Matthews and G. Stoltz, The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics, IMA J. Numer. Anal. 36(1), 13-79 (2016) preprint
  • G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre and G. Stoltz, Convergence of the Wang-Landau algorithm, Math. Comput. 84(295), 2297-2327 (2015) preprint
  • M. Dobson, F. Legoll, T. Lelièvre and G. Stoltz, Derivation of Langevin dynamics in a nonzero background flow field, M2AN 47, 1583–1626 (2013) preprint
  • A. Iacobucci, F. Legoll, S. Olla and G.Stoltz, Negative thermal conductivity of chains of rotors with mechanical forcing, Phys. Rev. E 84 061108 (2011) preprint
  • R. Joubaud and G. Stoltz, Nonequilibrium shear viscosity computations with Langevin dynamics, Multiscale Model. Sim. 10, 191-216 (2012) (preprint, erratum of the published version)
  • C. Bernardin and G. Stoltz, Anomalous diffusion for a class of systems with two conserved quantities, Nonlinearity 25, 1099- 1133 (2012) preprint
  • T. Lelièvre, M. Rousset and G. Stoltz, Langevin dynamics with constraints and computation of free energy differences, Math. Comput. 81, 2071-2125 (2012) preprint
  • N. Chopin, T. Lelièvre and G. Stoltz, Free energy methods for efficient exploration of mixture posterior densities, Statist. Comput. 22(4), 897-916 (2012) preprint
  • A. Iacobucci, F. Legoll, S. Olla, G. Stoltz, Thermal conductivity of the Toda lattice with conservative noise, J. Stat. Phys. 140(2), 336-348 (2010) preprint
  • B. Dickson, F. Legoll, T. Lelièvre, G. Stoltz, P. Fleurat-Lessard, Free energy calculations: An efficient adaptive biasing potential method, J. Phys. Chem. B 114(17), 5823–5830 (2010) preprint
  • J.B. Maillet and G. Stoltz, Sampling constraints in average: The example of Hugoniot curves, Appl. Math. Res. Express 2008, abn:004 (2009) preprint
  • T. Lelièvre, M. Rousset and G. Stoltz, Long-time convergence of an Adaptive Biasing Force method, Nonlinearity 21, 1155-1181 (2008) preprint
  • T. Lelièvre, M. Rousset and G. Stoltz, Computation of free energy profiles with parallel adaptive dynamics, J. Chem. Phys. 126, 134111 (2007) preprint
  • G. Stoltz, Path sampling with stochastic dynamics: some new algorithms, J. Comput. Phys. 225, 491-508 (2007) preprint
  • T. Lelièvre, M. Rousset and G. Stoltz, Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case, J. Comput. Phys. 222(2), 624-643 (2007) preprint
  • M. Rousset and G. Stoltz, An interacting particle system approach for molecular dynamics, J. Stat. Phys. 123(6), 1251-1272 (2006) preprint
  • E. Cancès, F. Legoll, and G. Stoltz, Theoretical and numerical comparison of some sampling methods, M2AN 41(2) 351-390(2007) preprint

Quantum chemistry and quantum physics

  • É. Cancès, A. Levitt, G. Panati and G. Stoltz, Robust determination of maximally-localized Wannier functions, Phys. Rev. B 95, 075114 (2017) preprint
  • E. Cancès, D. Gontier and G. Stoltz, A mathematical analysis of the GW0 method for computing electronic excited state energies of molecules, Rev. Math. Phys. 28(4) 1650008 (2016) preprint
  • E. Cancès and G. Stoltz, A mathematical formulation of the random phase approximation for crystals, Ann. I. H. Poincare-An. 29(6) 887-925 (2012) pdf
  • Christian Brouder, Gianluca Panati and Gabriel Stoltz, Gell-Mann and Low formula for degenerate unperturbed states, Ann. I. H. Poincare-Phy 10(7) 1285-1309 (2010) preprint
  • Christian Brouder, Gianluca Panati and Gabriel Stoltz, The Green function of degenerate systems, Phys. Rev. Lett. 103, 230401 (2009) preprint
  • Gabriel Stoltz, Natalio Mingo and Francesco Mauri, Reducing the thermal conductivity of carbon nanotubes below the random isotope limit, Phys. Rev. B 80, 113408 (2009) preprint
  • Gabriel Stoltz, Michele Lazzeri and Francesco Mauri,Thermal transport in isotopically disordered carbon nanotubes: a comparison between Green’s functions and Boltzmann approaches, J. Phys. Cond. Matter 21, 245302 (2009) pdf
  • Christian Brouder, Gabriel Stoltz and Gianluca Panati, Adiabatic approximation, Gell-Mann and Low theorem and degeneracies: A pedagogical example, Phys. Rev. A 78, 042102 (2008) pdf
  • E. Cancès, G. Stoltz, G. Scuseria, V. Staroverov and E. Davidson, Local exchange potentials for electronic structure calculations, MathS In Action 2, 1-42 (2009) link, preprint
  • A.F. Izmaylov, V.N. Staroverov, G. Scuseria, E.R. Davidson, G. Stoltz, and E. Cancès, The effective local potential method: Implementation for molecules and relation to approximate optimized effective potential techniques, J. Chem. Phys. 126, 084107 (2007)
  • A. Scemama, T. Lelièvre, G. Stoltz, E. Cancès, M. Caffarel, An efficient sampling algorithm for Variational Monte Carlo, J. Chem. Phys. 125, 114105 (2006) preprint
  • E. Cancès, M. Lewin and G. Stoltz, The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach, J. Chem. Phys. 125, 064101 (2006) preprint

Shock waves and coarse-grained dynamics

  • G. Faure and G. Stoltz, Stable and accurate schemes for smoothed dissipative particle dynamics, Appl. Math. Mech.-Engl. 39(1), 83-102 (2018) preprint
  • G. Stoltz, Stable schemes for dissipative particle dynamics with conserved energy, J. Comput. Phys. 340, 451–469 (2017) preprint
  • P. Terrier, M. Athènes, T. Jourdan, G. Adjanor, G. Stoltz, Cluster dynamics modelling of materials: a new hybrid deterministic/stochastic coupling approach, J. Comput. Phys. 350, 280-295 (2017) pdf
  • G. Faure, J. Roussel, J.-B. Maillet and G. Stoltz, Size consistency in Smoothed Dissipative Particle Dynamics, Phys. Rev. E 94 043305 (2016) preprint
  • T. Jourdan, G. Stoltz, F. Legoll and L. Monasse, An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach, Comput. Phys. Commun. 207 170-178 (2016) preprint
  • A.-A. Homman, J.-B. Maillet, J. Roussel and G. Stoltz, New parallelizable schemes for integrating the Dissipative Particle Dynamics with Energy Conservation, J. Chem. Phys. 144 024112 (2016) preprint
  • G. Ferre, J.-B. Maillet and G. Stoltz, Permutation-invariant distance between atomic configurations, J. Chem. Phys. 143 104114 (2015) preprint
  • A.-A. Homman, E. Bourasseau, G. Stoltz, P. Malfreyt, L. Strafella and A. Ghoufi, Surface tension of spherical drops from surface of tension, J. Chem. Phys. 140 034110 (2014) link
  • G. Faure, J.-B. Maillet and G. Stoltz, Local density dependent potential for compressible mesoparticles, J. Chem. Phys. 140 114105 (2014) preprint
  • J.-B. Maillet, G. Vallverdu, N.Desbiens and G. Stoltz, Molecular Simulations of Shock to Detonation Transition in Nitromethane, Europhys. Lett. 96 68007 (2011) preprint
  • E. Bourasseau, J.-B. Maillet, N.Desbiens and G. Stoltz, Microscopic calculations of Hugoniot curves of neat TATB and of its detonation products, J. Phys. Chem. A 115(39) 10729-10737 (2011) preprint
  • J.-B. Maillet, E. Bourasseau, L. Soulard, J. Clerouin and G. Stoltz, Constant entropy sampling and release waves of shock compressions, Phys. Rev. E 80, 021135 (2009) preprint
  • J.-B. Maillet, L. Soulard and G. Stoltz, A reduced model for shock and detonation waves. 2. The reactive case, Europhys. Lett. 78(6), 68001(2007) preprint
  • G. Stoltz, A reduced model for shock and detonation waves. 1. The inert case, Europhys. Lett. 76(5), 849-855 (2006) preprint (Erratum: Europhys. Lett., 77(3), 39901 (2007))
  • G. Stoltz, Shock waves in an augmented one-dimensional chain, Nonlinearity 18, 1967-1985 (2005) preprint

PhD & Habilitation thesis

You will find here an electronic version of the manuscript of my habilitation thesis (abstract, english except for the first pages…), as well as an electronic version of my PhD thesis (abstract, english, french).