Lindblad Research Paper

Right, on to quantum. I'll get to what a Lindblad is, but some context is needed for it to be meaningful. None of the below is strictly true, because QM (and physics in general) is written in mathematics, not words - we use symbols to generate predictive models, and then we try to feel out an ontology using language, hoping that whatever ontology we pin to these symbols will motivate the next mathematical theory. In other words, just like your high school physics lessons, this is at best an approximation to the truth:

Quantum mechanics, with its superposition states, entanglement, and strange stuff (colloquially referred to as 'quantum woooo') is a theory of physics that is experimentally verifiable, describes elements of nature that we have already observed (post-hoc), and has successfully predicted elements of nature that we had not observed, but have since gone on to verify (anti-matter, for example). So it's a theory of some things (definitely not everything) that is very well tested and
Now, the Hamiltonian evolution of a quantum state (its evolution in time) is described by the Von Neumann equation you sent earlier (basically it's a form of the Schrodinger equation); it's basically an 'ideal' equation, where there's no bath, and the information contained by the system is unchanged.

In order to model a system and environment, we create a quantum master equation, which is the Von Neumann equation with bits stuck on the end (just like adding air resistance to a Newtonian model in free space). These bits often take the form of Lindblad super-operators. Which are bits that satisfy a set of mathematical constraints that guarantee the state remains physical under the influence of the environment (no negative energy or other weird things). Which in turn lets you write your master equation as a Lindblad equation. Take a look at: