Any long-time limit of reversible area-interaction birth-death dynamics starting from a regular measure is shown to be a Gibbs point process, via relative-entropy dissipation.
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Reversible birth-and-death dynamics in continuum: free-energy dissipation and attractor properties
Any long-time limit of reversible area-interaction birth-death dynamics starting from a regular measure is shown to be a Gibbs point process, via relative-entropy dissipation.