Sharp Convergence to Equilibrium for the SSEP with Reservoirs

2021/10/12 by Gonçalves, Patrícia, Jara, Milton, Marinho, Rodrigo +1 · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2110.06353

Abstract

We consider the symmetric simple exclusion process evolving on the interval of length n-1 in contact with reservoirs of density ρ∈ (0,1) at the boundary. We use Yau's relative entropy method to show that if the initial measure is associated with a profile u₀:[0,1] → (0,1), then at explicit times tⁿ(b) that depend on u₀, the distance to equilibrium, in total variation distance, converges, as n → ∞, to a profile \mathcal G(γe^-b). The parameter γ also depends on the initial profile u₀ and \mathcal G(m) stands for the total variation distance ‖\mathcal N (m,1) - \mathcal N(0,1)‖_TV.

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