# 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

#### Citations

##### Publications citing this paper.
SHOWING 1-4 OF 4 CITATIONS

VIEW 2 EXCERPTS
CITES METHODS

VIEW 2 EXCERPTS
CITES METHODS

VIEW 1 EXCERPT
CITES BACKGROUND

## Sensitive Dependence of Gibbs Measures at Low Temperatures

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 30 REFERENCES

O. Jenkinson
• Series A,
• 2006