# the convergence speed for a Markov chain

For a metropolis hastings algorithm, suppose that the stationary distribution is defined as the Gibbs Boltzmann distribution $$\pi_T(x)= \frac{1}{Z_T}e^{-\frac{V(x)}{T} }$$ where $$Z_T = \sum_{y\in V} e^{-\frac{V(y)}{T}}$$.

It is known why there is no need to calculate the normalizing constant $$Z_T$$ for the posterior distribution but I am wondering if there are methods or articles presented how to approximate it especially for metropolis hastings in applications because sometimes it appears again when computing the convergence speed!