Dilation of stochastic matrices by coarse graining
Mathematical Physics
2021-06-08 v1 math.MP
Abstract
We consider two different ways of representing stochastic matrices by bi-stochastic ones acting on a larger probability space, referred to as ``dilation by uniform coarse graining" and ``environmental dilation". The latter is motivated by analogy to the dilation of operations in quantum theory. Both types of dilation can be viewed as special cases of a general ``dilation by coarse graining". We also discuss the entropy balance and illustrate our results, among others, by an example of a stochastic -matrix, which serves as a simplified model of the conditional action of Maxwell's demon.
Cite
@article{arxiv.2106.03513,
title = {Dilation of stochastic matrices by coarse graining},
author = {Heinz-Jürgen Schmidt},
journal= {arXiv preprint arXiv:2106.03513},
year = {2021}
}