**Free energy and statistical mechanics of driven systems**

Many molecular systems display a huge range of time scales. Typically the systems are subject to small noise (e.g., from the environment) that induces events which are rare with respect to the time scale of the system’s internal vibrations. In thermal equilibrium, the time scales between the slowest processes and the fastest vibrations easily span 15 orders of magnitude where the latter limits the admissible time step in any numerical simulation. Building up statistics on the rare events by direct numerical simulation is therefore unfeasible. By suitable driving the rare events can be forced, however, at the price of biasing the system’s thermodynamic equilibrium. The goal of the project is to better understand the large deviations statistics of diffusive systems under driving and to design steering protocols that are optimal in the sense that they minimally perturb the dynamics and give rise to robust numerical estimators for equilibrium expectations.

The project is funded through the "Center for Scientific Simulation" (CSS).

**Selected Publications**

- J. Latorre, C. Hartmann, Ch. Schütte (2010), Free energy computation by controlled Langevin processes, Procedia Computer Science 1, pp. 1591-1600

- C. Hartmann, Ch. Schütte and G. Ciccotti (2010), On the linear response of mechanical systems with constraints, J. Chem. Phys. 132, 111103

- C. Hartmann, J. Latorre (2010), Computing free energy differences using conditioned diffusions, submitted to Proceedings of the 11th Granada Seminar on Computational Physics

- Schuette, Ch.and Winkelmann, St. and Hartmann, Carsten, (2011) Optimal control of molecular dynamics using Markov state models. Submitted to Mathematical Programming, Series B

- Walter, J. and Hartmann, C. and Maddocks, J. (2011) /Ambient space formulations and statistical mechanics of holonomically constrained Langevin systems./

http://publications.mi.fu-berlin.de/1078/ Eur. Phys. J. ST . (In Press)

- Hartmann, C. (2011) /Balanced model reduction of partially-observed Langevin processes: an averaging principle./ http://publications.mi.fu-berlin.de/802/ Math. Comput. Model. Dyn. Syst., 17 (5). pp. 463-490.

Head:

Christof Schütte

**Project researchers**

Carsten Hartmann, Juan Latorre,

Christof Schütte

Cooperations:

G. Ciccotti (Rome), Thomas Speck (Berkeley)