On the equivalence between Bernoulli dynamical systems and stochastic Markov processes

We extend to Bernoulli systems the explicit construction (elaborated previously for the baker transformation) of non-unitary, invertible transformations Λ, which associate Markovian processes admitting an $\text{H}$-theorem with the unitary dynamical group, through a similarity relation. We characterize the symmetries of the Bernoulli system as well as those of the associated Markov processes and provide examples of symmetry breaking under the passage, through a Λ transformation, from Bernoulli systems to stochastic Markov processes.