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A derivation of the master equation from path entropy maximization
1Department of Bioinformatics and Life Science, Soongsil University, Seoul, South Korea. jul@ssu.ac.kr
The Journal of Chemical Physics
|August 28, 2012
Summary
This study derives nth-order Markov processes and the master equation as unique solutions to an inverse problem, offering a rigorous justification for stochastic models.
Area of Science:
- Physics
- Mathematics
- Computational Science
Background:
- Master equations and Markov processes are standard models for stochastic processes.
- Current justifications rely on randomization and coarse-graining assumptions.
Purpose of the Study:
- To derive nth-order Markov processes and the master equation from an inverse problem.
- To provide a rigorous alternative justification for stochastic models.
- To systematically generalize existing stochastic models.
Main Methods:
- Formulating an inverse problem to derive stochastic models.
- Applying maximum entropy principles to underdetermined problems.
- Deriving nth-order Markov processes and the master equation.
Main Results:
- Nth-order Markov processes and the master equation are unique solutions to the inverse problem.
- Maximum entropy selection yields nth-order Markov processes for underdetermined constraints.
- A systematic method for generalizing stochastic models is provided.
Conclusions:
- The study offers a rigorous, principle-based derivation of master equations and Markov processes.
- Maximum entropy provides a principled approach to selecting stochastic models.
- This work enables systematic generalization of established stochastic modeling techniques.
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