Transport processes in Newtonin and non-Newotonian fluids and fluctuation-dissipation theorems

The subject of this paper is molecular modelling of the transport processes in liquids including nanofluids. The weak and strong nonequilibrium processes are considered. In the first case, the corresponding fluctuation-dissipation theorems are formulated. These theorems determine the relation between the dissipative processes and equilibrium thermal fluctuations of the mass, momentum, and energy in the molecular system. Two different formulations of these theorem are discussed in detail. Various systems are considered: molecular liquids, nanofluids, turbulent liquids, fluids in confined conditions, and microviscosity in biomembranes. In the last part the nonlinear transport processes and rheology of the non-Newtonian fluids are discussed.