Dilation of stochastic matrices by coarse graining
Abstract
We consider two different ways of representing stochastic matrices by bistochastic 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 $4\times 4$matrix, which serves as a simplified model of the conditional action of Maxwell's demon.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.03513
 Bibcode:
 2021arXiv210603513S
 Keywords:

 Mathematical Physics