Negative entropy, zero temperature and Markov chains on the interval

@article{Lopes2009NegativeEZ,
  title={Negative entropy, zero temperature and Markov chains on the interval},
  author={Artur O. Lopes and Joana Mohr and Rafael R. Souza and Ph. Thieullen},
  journal={Bulletin of the Brazilian Mathematical Society, New Series},
  year={2009},
  volume={40},
  pages={1-52}
}
AbstractWe consider ergodic optimization for the shift map on the modified Bernoulli space σ: [0, 1]ℕ → [0, 1]ℕ, where [0, 1] is the unit closed interval, and the potential A: [0, 1]ℕ → ℝ considered depends on the two first coordinates of [0, 1]ℕ. We are interested in finding stationary Markov probabilities µ∞ on [0, 1]ℕ that maximize the value ∫ Adµ, among all stationary (i.e. σ-invariant) probabilities µ on [0, 1]ℕ. This problem correspond in Statistical Mechanics to the zero temperature case… CONTINUE READING