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Does the definition of mixing time work for general non-Markovian processes?

A definition of the mixing time for Markov chains is given by \begin{equation} \tau_{\text{mix}}\equiv\inf{\{t>0: \sup_i\left\vert \frac{\boldsymbol{p}(t|p_j(0)=\delta_{ij})}{\boldsymbol{\pi}}-\...
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