TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Zhang, Wei T1 - Jarzynski's equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms JF - Journal of Statistical Physics N2 - In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality. Y1 - 2018 U6 - https://doi.org/10.1007/s10955-019-02286-4 VL - 175 IS - 6 SP - 1214 EP - 1261 ER - TY - JOUR A1 - Wang, Han A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Site, Luigi Delle T1 - Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique JF - Phys. Rev. X Y1 - 2013 U6 - https://doi.org/10.1103/PhysRevX.3.011018 VL - 3 SP - 011018 ER - TY - JOUR A1 - Horenko, Illia A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Noé, Frank T1 - Data-based Parameter Estimation of Generalized Multidimensional Langevin Processes JF - Phys. Rev. E Y1 - 2007 UR - http://publications.imp.fu-berlin.de/31/ U6 - https://doi.org/10.1103/PhysRevE.76.016706 VL - 76 IS - 01 SP - 016706 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Kalibaeva, G. A1 - Pierro, M. A1 - Ciccotti, Giovanni T1 - Fast Simulation of Polymer Chains JF - J. Chem. Phys. Y1 - 2009 UR - http://publications.imp.fu-berlin.de/18/ U6 - https://doi.org/10.1063/1.3110603 VL - 130 SP - 144101 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof T1 - Efficient rare event simulation by optimal nonequilibrium forcing JF - J. Stat. Mech. Theor. Exp. Y1 - 2012 UR - http://publications.imp.fu-berlin.de/1153/ U6 - https://doi.org/10.1088/1742-5468/2012/11/P11004 VL - 2012 SP - P11004 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Ciccotti, Giovanni T1 - On the linear response of mechanical systems with constraints JF - J. Chem. Phys. Y1 - 2010 UR - http://publications.imp.fu-berlin.de/794/ U6 - https://doi.org/10.1063/1.3354126 VL - 132 IS - 11 SP - 111103 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Vulcanov, V.-M. A1 - Schütte, Christof T1 - Balanced Truncation of Second Order Systems JF - Multiscale Model. Simul. Y1 - 2010 UR - http://publications.imp.fu-berlin.de/28/ U6 - https://doi.org/10.1137/080732717 VL - 8 IS - 4 SP - 1348 EP - 1367 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Schütte, Christof T1 - A Geometric Approach to Constrained Molecular Dynamics and Free Energy JF - Comm. Math. Sci. Y1 - 2005 UR - http://publications.imp.fu-berlin.de/48/ VL - 3 IS - 1 SP - 1 EP - 20 ER - TY - JOUR A1 - Schütte, Christof A1 - Noé, Frank A1 - Meerbach, E. A1 - Metzner, Ph. A1 - Hartmann, Carsten T1 - Conformation Dynamics JF - Proceedings of the 6th International Congress on Industrial and Applied Mathematics, I. Jeltsch and G. Wanner (eds.), Y1 - 2009 UR - http://publications.imp.fu-berlin.de/110/ U6 - https://doi.org/10.4171/056-1/15 SP - 297 EP - 335 PB - EMS publishing house ER - TY - JOUR A1 - Schütte, Christof A1 - Walter, J. A1 - Hartmann, Carsten A1 - Huisinga, Wilhelm T1 - An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations JF - Multiscale Model. Simul. Y1 - 2004 UR - http://publications.imp.fu-berlin.de/62/ U6 - https://doi.org/10.1137/030600308 VL - 2 IS - 3 SP - 501 EP - 526 ER -