Free Energy Computations: A Mathematical Perspective

Mathematical foundations for the Parallel Replica algorithm applied to the underdamped Langevin dynamics

Ramil, M., Tony Lelièvre, A., & Reygner, J. (2022) · MRS Communications · doi:10.1557/s43579-022-00207-3 · Cited by 1

Projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles

McGarrigle, E. C., Ceniceros, H. D., & Fredrickson, G. H. (2024) · Physical review. E · doi:10.1103/physreve.110.065308 · Cited by 1

A Hybrid OPES-eABF Framework for Efficient Exploration and Data-Driven Collective Variable Discovery in Complex Free-Energy Landscapes

Chakraborty, G., & Patra, N. (2025) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.5c02158 · Cited by 1

A systematic analysis of the memory term in coarse-grained models: The case of the Markovian approximation

Pasquale, N. D., Hudson, T., Icardi, M., Rovigatti, L., & Spinaci, M. (2022) · European Journal of Applied Mathematics · doi:10.1017/s0956792522000158 · Cited by 1

Bottom-Up Transient Time Models in Coarse-Graining Molecular Systems

Baxevani, G., Harmandaris, V., Kalligiannaki, E., & Tsantili, I. C. (2023) · Multiscale Modeling and Simulation · doi:10.1137/23m1548451 · Cited by 1

Deriving a GENERIC system from a Hamiltonian system

Mielke, A., Peletier, M. A., & Zimmer, J. (2025) · Archive for Rational Mechanics and Analysis · doi:10.1007/s00205-025-02119-7 · Cited by 1

Variance Reduction Result for a Projected Adaptive Biasing Force Method

Alrachid, H., & Tony Lelièvre, A. (2017) · SEMA SIMAI Springer series · doi:10.1007/978-3-319-49631-3_10 · Cited by 1

Strong convergence of a half-explicit Euler scheme for constrained stochastic mechanical systems

Lindner, F., & Stroot, H. (2020) · IMA Journal of Numerical Analysis · doi:10.1093/imanum/draa009 · Cited by 1

Mathematical Foundations of Accelerated Molecular Dynamics Methods

Tony Lelièvre, A. (2020) · Springer eBooks · doi:10.1007/978-3-319-44677-6_27 · Cited by 1

Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects

Gorynina, O., Legoll, F., Tony Lelièvre, A., & Pérez, D. (2023) · Comptes Rendus Mécanique · doi:10.5802/crmeca.220 · Cited by 1

Switched diffusion processes for non-convex optimization and saddle points search

Journel, L., & Monmarché, P. (2023) · Statistics and Computing · doi:10.1007/s11222-023-10315-2 · Cited by 1

Randomized time Riemannian Manifold Hamiltonian Monte Carlo

Whalley, P. A., Paulin, D., & Leimkuhler, B. (2023) · Statistics and Computing · doi:10.1007/s11222-023-10303-6 · Cited by 1

An Energy-Based Model Approach to Rare Event Probability Estimation

Friedli, L., Ginsbourger, D., Arnaud Doucet, B., & Linde, N. (2025) · SIAM/ASA Journal on Uncertainty Quantification · doi:10.1137/23m1605065 · Cited by 1

Sampling Techniques for Computational Statistical Physics

Leimkuhler, B., & Stoltz, G. (2015) · Springer eBooks · doi:10.1007/978-3-540-70529-1_268 · Cited by 1

Étude probabiliste de systèmes de particules en interaction : applications à la simulation moléculaire

Roux, R. (2010) · doi:10.70675/b8f01935z98cbz4c05z89aaz6010b8819eda · Cited by 1

Development of new numerical integration schemes of.multiscale coarse-graining methods

Homman, A. (2016) · doi:10.70675/30931abfz8935z4f4czbbf2z4e14768383f6 · Cited by 1

Stochastic Differential Equations

Lord, G. J. (2015) · Wiley eBooks · doi:10.1002/3527600434.eap725

Machine learning in multiscale modeling and simulations of molecular systems

Hashemian, B. (2015) · doi:10.5821/dissertation-2117-95711

Tunnel effect for semiclassical random walk

Bony, J., Hérau, F., & Michel, L. (2014) · Journées Équations aux dérivées partielles · doi:10.5802/jedp.109

A FORWARD EQUATION FOR COMPUTING DERIVATIVES EXPOSURE

Lapeyre, B., & Taarit, M. I. (2019) · International Journal of Theoretical and Applied Finance · doi:10.1142/s0219024919500158

Molecular Simulations of Supramolecular Architectures

Cai, W., & Fu, H. (2019) · Springer eBooks · doi:10.1007/978-981-13-1744-6_45-1

The adaptive biasing force algorithm with non-conservative forces and related topics

Tony Lelièvre, A., Maurin, L., & Monmarché, P. (2022) · ESAIM Mathematical Modelling and Numerical Analysis · doi:10.1051/m2an/2022010

Calculation of Binding Free Energy and Kinetic Rates with Flexible Protein Docking

Tran, D. P., & Kitao, A. (2021) · Seibutsu Butsuri · doi:10.2142/biophys.61.398

Stochastic Systems

Kuehn, C. (2014) · Applied mathematical sciences · doi:10.1007/978-3-319-12316-5_15

Calculation of Ensemble Averages

Stoltz, G. (2015) · Springer eBooks · doi:10.1007/978-3-540-70529-1_265

Transition Pathways, Rare Events and Related Questions

Darve, E. (2015) · Springer eBooks · doi:10.1007/978-3-540-70529-1_266

Molecular Simulations of Supramolecular Architectures

Cai, W., & Fu, H. (2020) · Springer eBooks · doi:10.1007/978-981-15-2686-2_45

A New Approach for Estimating the Free Energy Differences among Multiple Thermodynamic States in Statistical Simulations

Yang, J., & Singer, S. J. (2023) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.3c00620

A Categorical Approach to Statistical Mechanics

Sergeant-Perthuis, G. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-38271-0_26

Sharp Spectral Gap of Adaptive Langevin Dynamics

Delande, L. (2025) · Asymptotic Analysis · doi:10.1177/09217134251317871

The quantum mechanical potential of mean force: density matrix formulation, estimators, and constrained path integral molecular dynamics integrators

Iouchtchenko, D., Bishop, K. P., & Roy, P. (2025) · Molecular Physics · doi:10.1080/00268976.2025.2577825

Computing Large Deviation Rate Functions of Entropy Production for Diffusion Processes by an Interacting Particle Method

Wu, Z., Raquépas, R., Xin, J. X., & Zhang, Z. (2025) · SIAM Journal on Scientific Computing · doi:10.1137/24m1720172

Thermodynamic framework for modeling social adoption in multi-agent systems

Giardini, G. S. Y., & daCunha, C. R. (2025) · Physical review. E · doi:10.1103/fps8-ltw5

Sharp Spectral Gap for Some Degenerate Witten Laplacians

Delande, L. (2026) · Annales Henri Poincaré · doi:10.1007/s00023-026-01673-4

Deterministic and stochastic methods for molecular simulation

Minoukadeh, K. (2010) · doi:10.70675/0b8d203az50b5z494bz835czdb7608616a3c

Exploring chemo-mechanical transduction in the myosin molecular motor through computer simulations

Blanc, F. E. C. (2018) · doi:10.70675/a34cebe7zaccaz4f65zbe18zbb32053df496

Weak over-damped asymptotic and variance reduction

Xu, Y. (2019) · doi:10.70675/666326e1zbc88z4610zbd3ezbe2ac988ec66

Random walks for estimating densities of states and the volume of convex bodies in high dimensional spaces

Chevallier, A. (2019) · doi:10.70675/dc48b44fzb334z42b3z9cf1z59e1ea57b1d6

Computer simulations to engineer PDZ-peptide recognition

Villa, F. (2018) · theses.fr (ABES) · doi:10.70675/73ac9057zc3bfz4912zbb3fz6b06f4a4e669

Adaptive biasing algorithms : mathematical analysis and applications in molecular dynamics

Maurin, L. (2021) · doi:10.70675/8d030170zb542z43f3z8ecfz023b75634f87

The influence of periodic edge conditions for the simulation of some quantities of interest for separative chemistry

de Guerny, A.-F. (2021) · doi:10.70675/b32431f1z4050z4e39zb647zd9231090e83b

Systems of particles in (singular) interaction : long time behavior and propagation of chaos

Bris, P. L. (2023) · doi:10.70675/b55df7cfz2fc7z4247za9cez86c6b0d8ae30

Modelling functions with kernels : from logistic regression to global optimisation

Marteau-Ferey, U. (2022) · theses.fr (ABES) · doi:10.70675/cd520bcbzc438z4b81za165ze38a48db32bb

Large scale Bayesian inference

Sekkat, I. (2022) · theses.fr (ABES) · doi:10.70675/c9e12d31z25edz46a7zb99fzbdd76e4db319

Numerical evaluation of Rényi entropy with path integrals

Srdinšek, M. (2023) · doi:10.70675/701196eezd03cz4671z8d45z6492afe498d7

Modeling and Standard Binding Free Energy Calculations of Complex Biological Objects

Blazhynska, M. (2023) · theses.fr (ABES) · doi:10.70675/48e8ac59z3fecz4841za036z40e6a446b0cc

Efficient computation of transport coefficients in molecular dynamics

Spacek, R. (2024) · doi:10.70675/d01b076fz20afz4179z9418z09e5e28eaa79

Sur les gaz de Coulomb et le transport optimal multimarge

Lelotte, R. (2023) · doi:10.70675/be1029f0zd58az415fz8847zc2557adefa96

Machine learning and adaptive sampling to predict finite-temperature properties in metallic materials at the atomic scale

Zhong, A. (2024) · doi:10.70675/bdc13f96z2dc5z47a7z9373zb8ff019acc4a

Long-time behavior of some Markov processes, and application to stochastic algorithms

Journel, L. (2024) · doi:10.70675/9a7124f0z9028z4a43zb0d9zd95770a91ee9

Relative Entropy Methods for the Approximation of Reactive Trajectories and Committor Functions

Earle, G., & Koten, B. V. (2026) · SIAM/ASA Journal on Uncertainty Quantification · doi:10.1137/25m1757708

A Force-Kernel Reformulation of the Extended-System Adaptive Biasing Force for Free-Energy Calculations

Kang, C., Verma, R., Sonpal, A., Shoji, A., Chipot, C. J., & Pfaendtner, J. (2026) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6c00879

Approximating Langevin Monte Carlo with ResNet-like Neural Network Architectures

Miranda, C., Schütte, J., Sommer, D., & Eigel, M. (2026) · International Journal of Applied and Computational Mathematics · doi:10.1007/s40819-026-02127-5 · Cited by 2

Free Energy Calculations

(2006) · Springer eBooks · doi:10.1007/1-4020-3587-x_14 · Cited by 74

Numerical Computations

(2006) · IMPERIAL COLLEGE PRESS eBooks · doi:10.1142/9781860949142_0006

Free Energy Simulations

Straatsma, T. P. (1998) · Wiley eBooks · doi:10.1002/0470845015.cfa012 · Cited by 3

Energy

(2011) · IMPERIAL COLLEGE PRESS eBooks · doi:10.1142/9781848165755_0006

Free energy

Ryabov, V. A. (2018) · Institute of Physics eBooks · doi:10.1088/978-0-7503-1341-4ch11