  We discuss the role of information entropy on the behaviour of random
processes, and how this might take effect in the dynamics of financial market
prices. We then go on to show how the Open Quantum Systems approach can be used
as a more flexible alternative to classical methods in terms of modelling the
entropy gain of a random process. We start by describing an open quantum system
that can be used to model the state of a financial market. We then go on to
show how to represent an essentially classical diffusion in this framework.
Finally, we show how by relaxing certain assumptions, one can generate
interesting and essentially non-classical results, which are highlighted
through numerical simulations.
