Through this paper we analyze the ergodic properties of continuous time Markov chains with values on the one-dimensional spin lattice {1, . . . , d}N (also known as the Bernoulli space). Initially, we consider as the infinitesimal generator the operator L = LA − I, where LA is a discrete time Ruelle operator (transfer operator), and A : {1, . . . , d}N →R is a given fixed Lipschitz function. The associated continuous time stationary Markov chain will define the a priori probability. Given a Lipschitz interaction V : {1, . . . , d}N →R, we are interested in Gibbs (equilibrium) state for such V . This will be another continuous time stationary Markov chain. In order to analyze this problem we will use a continuous time Ruelle operator (transfer operator) naturally associated to V . Among other things we will show that a continuous time Perron-Frobenius Theorem is true in the case V is a Lipschitz function. We also introduce an entropy, which is negative (see also Lopes et al. in Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature. Arxiv, 2012), and we consider a variational principle of pressure. Finally, we analyze large deviations properties for the empirical measure in the continuous time setting using results by Y. Kifer (Tamsui Oxf. J. Manag. Sci. 321(2):505- 524, 1990). In the last appendix of the paper we explain why the techniques we develop here have the capability to be applied to the analysis of convergence of a certain version of the Metropolis algorithm.< Réduire