caa a22 4500 467891915 CHVBK 20180406152751.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s10955-005-9003-9 doi (NATIONALLICENCE)springer-10.1007/s10955-005-9003-9 Towards a Theory of Transition Paths [Elektronische Daten] [Weinan E., Eric Vanden-Eijnden] We construct a statistical theory of reactive trajectories between two pre-specified sets A and B, i.e. the portionsof the path of a Markov process during which the path makes a transition from A to B. This problem is relevant e.g. in the context of metastability, in which case the two sets A and B are metastable sets, though the formalism we propose is independent of any such assumptions on A and B. We show that various probability distributions on the reactive trajectories can be expressed in terms of the equilibrium distribution of the process and the so-called committor functions which give the probability that the process reaches first B before reaching A, either backward or forward in time. Using these objects, we obtain (i) the distribution of reactive trajectories, which gives the proportion of time reactive trajectories spend in sets outside of A and B; (ii) the hitting point distribution of the reactive trajectories on a surface, which measures where the reactive trajectories hit the surface when they cross it; (iii) the last hitting point distribution of the reactive trajectories on the surface; (iv) the probability current of reactive trajectories, the integral of which on a surface gives the net average flux of reactive trajectories across this surface; (v) the average frequency of reactive trajectories, which gives the average number of transitions between A and B per unit of time; and (vi) the traffic distribution of reactive trajectories, which gives some information about the regions the reactive trajectories visit regardless of the time they spend in these regions. Springer Science + Business Media, Inc., 2006 Transition path theory nationallicence transition state theory nationallicence transition path sampling nationallicence matastability nationallicence reactive trajectories nationallicence transition pathways nationallicence E. Weinan Department of Mathematics and PACM, Princeton University, 08544, Princeton, NJ, USA aut Vanden-Eijnden Eric Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/3(2006-05-01), 503-523 0022-4715 123:3<503 2006 123 10955 https://doi.org/10.1007/s10955-005-9003-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-9003-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- E Weinan Department of Mathematics and PACM, Princeton University, 08544, Princeton, NJ, USA aut NATIONALLICENCE 700 1- Vanden-Eijnden Eric Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/3(2006-05-01), 503-523 0022-4715 123:3<503 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer