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

Journal of Statistical Physics
 Pub Date:
 March 2021
 DOI:
 10.1007/s10955021027251
 arXiv:
 arXiv:2012.03885
 Bibcode:
 2021JSP...182...44B
 Keywords:

 Repeated quantum measurements;
 Quantum instrument;
 Arrow of time;
 Matrix product measure;
 Hidden Markov model;
 Equilibrium state;
 NonGibbsian measure;
 Entropy production;
 Fluctuation relations;
 Large deviations;
 Hermodynamic formalism;
 Shift space;
 Mathematical Physics;
 Mathematics  Dynamical Systems;
 Mathematics  Probability;
 Quantum Physics
 EPrint:
 J. Stat. Phys. 182 (2021) 44