msmtools.flux.tpt(T, A, B, mu=None, qminus=None, qplus=None, rate_matrix=False)

Computes the A->B reactive flux using transition path theory (TPT)

  • T ((M, M) ndarray or scipy.sparse matrix) – Transition matrix (default) or Rate matrix (if rate_matrix=True)
  • A (array_like) – List of integer state labels for set A
  • B (array_like) – List of integer state labels for set B
  • mu ((M,) ndarray (optional)) – Stationary vector
  • qminus ((M,) ndarray (optional)) – Backward committor for A->B reaction
  • qplus ((M,) ndarray (optional)) – Forward committor for A-> B reaction
  • = False (rate_matrix) – By default (False), T is a transition matrix. If set to True, T is a rate matrix.

tpt – A python object containing the reactive A->B flux network and several additional quantities, such as stationary probability, committors and set definitions.

Return type:

msmtools.flux.ReactiveFlux object


The central object used in transition path theory is the forward and backward comittor function.

TPT (originally introduced in [1]) for continous systems has a discrete version outlined in [2]. Here, we use the transition matrix formulation described in [3].


[1]W. E and E. Vanden-Eijnden. Towards a theory of transition paths. J. Stat. Phys. 123: 503-523 (2006)
[2]P. Metzner, C. Schuette and E. Vanden-Eijnden. Transition Path Theory for Markov Jump Processes. Multiscale Model Simul 7: 1192-1219 (2009)
[3]F. Noe, Ch. Schuette, E. Vanden-Eijnden, L. Reich and T. Weikl: Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations. Proc. Natl. Acad. Sci. USA, 106, 19011-19016 (2009)