I have extensively worked with, and reviewed, the socalled projection technique, which allows for the systematic derivation of macroscopic transport equations from the underlying microscopic
dynamics. A thorough review, as well as three diverse applications, can be found in

J. Rau and B. Müller, From Reversible Quantum Microdynamics to Irreversible Quantum Transport, Physics Reports 272, 1 (1996) [doi][arXiv][pdf]

J. Rau, Pair production in the quantum Boltzmann equation, Physical Review D 50, 6911
(1994) [doi][arXiv][pdf]

P. Neu and J. Rau, Generalized Bloch equations for a strongly driven tunneling system, Physical
Review E 55, 2195 (1997) [doi][arXiv][pdf]

J. Rau, Geometric magnetism in classical transport theory, Physical Review E 56, 1295
(1997) [doi][arXiv][pdf]
Mathematical tools for estimating, on the basis of experimental data, the unknown parameters of a macroscopic equation of motion are discussed for two specific examples in
 J. Rau, Reconstructing the relaxation dynamics induced by an unknown heat bath, Physics Letters A 376, 370 (2012) [doi][arXiv][pdf]
 V. Bužek, P. Rapcan, J. Rau, M. Ziman, Direct estimation of decoherence rates, Physical Review A 86, 052109 (2012) [doi][arXiv][pdf]
To employ successive coarsegraining when going from the microscopic to the macroscopic realm, is a crucial idea shared by both the abovementioned projection technique and renormalization
group theory. Indeed, the two are intimately related, as I have argued in

J. Müller and J. Rau, Renormalization by Projection: On the Equivalence of the BlochFeshbach Formalism and Wilson's Renormalization, Physics Letters B 386, 274
(1996) [doi][arXiv][pdf]

J. Rau, Transport theory yields renormalization group equations, Physical Review E 55, 5147 (1997) [doi][arXiv][pdf]