On Entropy Production of Repeated Quantum Measurements II. Examples

We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed a previous work by studying examples instruments displaying various interesting phenomena and singularities. emphasize role thermodynamic formalism, give many whose resulting probability measures on space infinite sequences outcomes (shift space) do not have (weak) Gibbs property. also discuss physically relevant where rate satisfies large deviation principle but fails to obey central limit theorem fluctuation–dissipation theorem. Throughout analysis, we explore connections with other, priori unrelated topics like functions Markov chains, hidden models, matrix products number theory.