# Quantum Markov Semigroups

Quantum Markov semigroups are the natural mathematical objects for modelling the irreversible evolution of open quantum systems. This is governed by the so-called master equations whose solution is given by a quantum Markov semigroup. From a mathematical point of view, they can be viewed as a non-commutative generalisation of classical Markov semigroups acting on a commutative algebra (function space) [FSU17, BF17, CSU17, AFQ16, FR16, DFSU16, BSF15, FM15, FR15, AFR14, Fa04, CF03, FR03, AF02, CF00, CFL00, Fa99, CF98].