  Reaction-diffusion processes are the foundational model for a diverse range
of complex systems, ranging from biochemical reactions to social agent-based
phenomena. The underlying dynamics of these systems occur at the individual
particle/agent level, and in realistic applications, they often display
interaction with their environment through energy or material exchange with a
reservoir. This requires intricate mathematical considerations, especially in
the case of material exchange since the varying number of particles/agents
results in ``on-the-fly'' modification of the system dimension. In this work,
we first overview the probabilistic description of reaction-diffusion processes
at the particle level, which readily handles varying numbers of particles. We
then extend this model to consistently incorporate interactions with
macroscopic material reservoirs. Based on the resulting expressions, we bridge
the probabilistic description with macroscopic concentration-based descriptions
for linear and nonlinear reaction-diffusion systems, as well as for an
archetypal open reaction-diffusion system. This establishes a methodological
workflow to bridge particle-based probabilistic descriptions with macroscopic
concentration-based descriptions of reaction-diffusion in open settings, laying
the foundations for a multiscale theoretical framework upon which to construct
theory and simulation schemes that are consistent across scales.
