Exact Evolution Law for Canonical Path Ensembles with a Variance Controlled Precision Regime for Self-Organization
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908922419347456 |
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| author | Georgiev, Georgi Yordanov |
| author_facet | Georgiev, Georgi Yordanov |
| contents | Self-organizing open systems sustained by source--sink fluxes transform stochastic motion into ordered behavior, yet a general dynamical criterion governing this transformation has not been established. Building on a stochastic--dissipative path-ensemble formulation, this work derives an exact kinematic law for evolving canonical path ensembles under time-dependent parameter variation, decomposing the dynamics of the average stochastic action into contributions from selectivity modulation and structural deformation. In the precision-driven regime, the evolution closes: the rate of change is governed by the variance, yielding strict monotonicity under increasing selectivity, plateaus under stationary selectivity, and broadening under decreasing selectivity. Self-organization corresponds to endogenous, feedback-driven parameter evolution that reduces the average action, with the precision-driven regime providing a Lyapunov realization, while more general structural evolution yields system-dependent behavior; externally prescribed variation corresponds to controlled evolution. These results establish an exact ensemble-level law for organization in open stochastic systems with directly testable signatures in measurable statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Evolution Law for Canonical Path Ensembles with a Variance Controlled Precision Regime for Self-Organization Georgiev, Georgi Yordanov Adaptation and Self-Organizing Systems 82C05 Self-organizing open systems sustained by source--sink fluxes transform stochastic motion into ordered behavior, yet a general dynamical criterion governing this transformation has not been established. Building on a stochastic--dissipative path-ensemble formulation, this work derives an exact kinematic law for evolving canonical path ensembles under time-dependent parameter variation, decomposing the dynamics of the average stochastic action into contributions from selectivity modulation and structural deformation. In the precision-driven regime, the evolution closes: the rate of change is governed by the variance, yielding strict monotonicity under increasing selectivity, plateaus under stationary selectivity, and broadening under decreasing selectivity. Self-organization corresponds to endogenous, feedback-driven parameter evolution that reduces the average action, with the precision-driven regime providing a Lyapunov realization, while more general structural evolution yields system-dependent behavior; externally prescribed variation corresponds to controlled evolution. These results establish an exact ensemble-level law for organization in open stochastic systems with directly testable signatures in measurable statistics. |
| title | Exact Evolution Law for Canonical Path Ensembles with a Variance Controlled Precision Regime for Self-Organization |
| topic | Adaptation and Self-Organizing Systems 82C05 |
| url | https://arxiv.org/abs/2507.02209 |