Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Path summation formulation of the master equation.

Sean X Sun1

  • 1Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.

Physical Review Letters
|June 29, 2006
PubMed
Summary

Researchers derived an exact formula for Markovian path probabilities in discrete systems. This finding aids in analyzing complex reaction networks and satisfies the fluctuation theorem.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Whole organism 3D mapping reveals universal branching topology and biophysical optimization governs vascular and nervous system development.

bioRxiv : the preprint server for biology·2026
Same author

Cell-nanoplastics association impacts cell proliferation and motility.

bioRxiv : the preprint server for biology·2026
Same author

Hypoxia restores the acidosis-induced inhibition of cancer cell dissemination.

Cell reports·2026
Same author

Acute priming using elevated fluid viscosity recovers '<i>young-like</i>' single-cell surveillance behaviors in aged human T cells.

bioRxiv : the preprint server for biology·2026
Same author

From Decay to Rhythm: Coherent Biological Oscillators Require More Than Chemistry Alone.

bioRxiv : the preprint server for biology·2026
Same author

Cancer cells surviving cisplatin chemotherapy increase stress-induced OMA1 activity and mitochondrial fragmentation.

Scientific reports·2026

Area of Science:

  • Statistical mechanics
  • Physical chemistry
  • Computational biology

Background:

  • Markovian dynamics, described by the kinetic master equation, is fundamental across sciences.
  • Analyzing complex reaction networks often requires efficient computational methods.

Purpose of the Study:

  • To derive an exact expression for Markovian path probabilities in discrete state spaces.
  • To develop a novel computational approach for analyzing complex reaction networks.

Main Methods:

  • Derivation of exact path probability expressions for Markovian dynamics.
  • Summation of probabilities for paths with repeated state visits.
  • Formulation of transition probabilities as sums over all connecting paths.

Main Results:

  • An exact formula for Markovian path probabilities was obtained.
  • The derived probabilities satisfy the fluctuation theorem.
  • A path space Monte Carlo procedure was proposed as an alternative analysis algorithm.

Conclusions:

  • The derived path probabilities offer a new perspective on Markovian dynamics.
  • The proposed Monte Carlo method provides an efficient alternative for analyzing complex reaction networks.

Related Experiment Videos