Dynamical Gibbs Variational Principles for Irreversible Interacting Particle Systems with Applications to Attractor Properties
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916975130705920 |
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| author | Jahnel, Benedikt Köppl, Jonas |
| author_facet | Jahnel, Benedikt Köppl, Jonas |
| contents | We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove, that zero relative entropy loss of a translation-invariant measure implies, that the measure is Gibbs w.r.t. the same specification as the time-stationary Gibbs measure. As an application, we obtain the attractor property for irreversible interacting particle systems, which says that any weak limit point of any trajectory of translation-invariant measures is a Gibbs measure w.r.t. the same specification as the time-stationary measure. This extends previously known results to fairly general irreversible interacting particle systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_02738 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dynamical Gibbs Variational Principles for Irreversible Interacting Particle Systems with Applications to Attractor Properties Jahnel, Benedikt Köppl, Jonas Probability Primary 82C20, secondary 60K35 We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove, that zero relative entropy loss of a translation-invariant measure implies, that the measure is Gibbs w.r.t. the same specification as the time-stationary Gibbs measure. As an application, we obtain the attractor property for irreversible interacting particle systems, which says that any weak limit point of any trajectory of translation-invariant measures is a Gibbs measure w.r.t. the same specification as the time-stationary measure. This extends previously known results to fairly general irreversible interacting particle systems. |
| title | Dynamical Gibbs Variational Principles for Irreversible Interacting Particle Systems with Applications to Attractor Properties |
| topic | Probability Primary 82C20, secondary 60K35 |
| url | https://arxiv.org/abs/2205.02738 |