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In this chapter, we study KCM with initial state not distributed according to the stationary measure. We start by presenting detailed results on the East model, illustrating the kind of results one would like: exponential convergence to equilibrium after a temperature quench, mixing time cutoff in finite volume, etc. We then treat KCM in full generality at the cost of weakening the results. We conclude with open problems, such as bringing the two aspects above together, and some additional out-of-equilibrium settings. This chapter is independent from Chaps.  4 – 6 .

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Out of Equilibrium

  • 章节

  • 发表日期：

    2025年

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  • Ivailo Hartarsky,
  • Cristina Toninelli

摘要

In this chapter, we study KCM with initial state not distributed according to the stationary measure. We start by presenting detailed results on the East model, illustrating the kind of results one would like: exponential convergence to equilibrium after a temperature quench, mixing time cutoff in finite volume, etc. We then treat KCM in full generality at the cost of weakening the results. We conclude with open problems, such as bringing the two aspects above together, and some additional out-of-equilibrium settings. This chapter is independent from Chaps.  4 – 6 .