Closure–Leakage Constraints on Structural Stability and Metastability: A Thermodynamic Inequality for Persistent Patterns
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866901235040256000 |
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| author | Mullaveedu, Bubusuhas |
| author_facet | Mullaveedu, Bubusuhas |
| contents | <p>This work introduces a minimal structural stability constraint for persistent patterns in open dynamical systems. We formalize the balance between reinforcement ("closure") and dissipation ("leakage") as a rate inequality and show that this condition defines a stability gate for nonzero order-parameter domains.</p> <p>The closure–leakage balance is embedded into a general dynamical framework and connected to non-equilibrium thermodynamic bookkeeping via entropy production. A Lyapunov-functional construction demonstrates sufficient conditions for asymptotic stability and quantifies metastable lifetimes near the persistence threshold.</p> <p>A worked two-state Markov reinforcement model and a coarse-grained logistic model illustrate (i) emergence of stable nonzero density and (ii) scaling of relaxation time and lifetime with the net persistence rate. The framework yields falsifiable predictions including lifetime scaling near stability boundaries and dissipation bounds required for maintaining persistent structure in driven open media.</p> <p>The results provide a thermodynamically consistent constraint principle for pattern persistence applicable across physics, materials, and open complex systems.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18637699 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Closure–Leakage Constraints on Structural Stability and Metastability: A Thermodynamic Inequality for Persistent Patterns Mullaveedu, Bubusuhas open systems nonequilibrium thermodynamics metastability Lyapunov stability pattern formation entropy production dissipative structures nonlinear dynamics stability thresholds <p>This work introduces a minimal structural stability constraint for persistent patterns in open dynamical systems. We formalize the balance between reinforcement ("closure") and dissipation ("leakage") as a rate inequality and show that this condition defines a stability gate for nonzero order-parameter domains.</p> <p>The closure–leakage balance is embedded into a general dynamical framework and connected to non-equilibrium thermodynamic bookkeeping via entropy production. A Lyapunov-functional construction demonstrates sufficient conditions for asymptotic stability and quantifies metastable lifetimes near the persistence threshold.</p> <p>A worked two-state Markov reinforcement model and a coarse-grained logistic model illustrate (i) emergence of stable nonzero density and (ii) scaling of relaxation time and lifetime with the net persistence rate. The framework yields falsifiable predictions including lifetime scaling near stability boundaries and dissipation bounds required for maintaining persistent structure in driven open media.</p> <p>The results provide a thermodynamically consistent constraint principle for pattern persistence applicable across physics, materials, and open complex systems.</p> |
| title | Closure–Leakage Constraints on Structural Stability and Metastability: A Thermodynamic Inequality for Persistent Patterns |
| topic | open systems nonequilibrium thermodynamics metastability Lyapunov stability pattern formation entropy production dissipative structures nonlinear dynamics stability thresholds |
| url | https://doi.org/10.5281/zenodo.18637699 |