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Stationary properties of maximum-entropy random walks
1Department of Systems Biology, Columbia University, New York, New York 10032, United States.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
Maximum-entropy inference in complex systems is advanced by studying path-dependent constraints in stochastic processes. The resulting stationary distribution differs from the Boltzmann distribution, balancing path options and rules.
Area of Science:
- Statistical mechanics
- Complex systems analysis
- Stochastic processes
Background:
- Maximum-entropy (ME) inference is widely used for complex systems.
- The impact of state space topology and path-dependent constraints on ME-inferred probabilities in stochastic systems is not well understood.
Purpose of the Study:
- To derive transition probabilities and stationary distribution for a maximum path entropy Markov process.
- To investigate the influence of state- and path-dependent constraints on these probabilities.
Main Methods:
- Derivation of transition probabilities for a maximum path entropy Markov process.
- Analysis of stationary distribution under state- and path-dependent constraints.
- Illustration using particle diffusion on a 2D landscape.
Main Results:
- The stationary distribution significantly deviates from the Boltzmann distribution.
- This deviation arises from a competition between path multiplicity and imposed constraints.
- The study provides insights into how topology and path constraints shape system dynamics.
Conclusions:
- The findings clarify the role of path-dependent constraints in maximum-entropy inference for stochastic systems.
- The derived stationary distribution offers a more accurate representation than the Boltzmann distribution in such cases.
- This work connects maximum path entropy methods with path integral approaches to diffusion.
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