Development of the new approach to describe turbulent motions in condensed matter on the basis of nonlocal modeling highly non-equilibrium processes in open systems is performed in parallel with experimental studying the mesostructure in dynamically deformed solids. The shock-induced mesostructure formation inside the propagating waveform registered in real time allows the transient stages of non-equilibrium processes to be qualitative and quantitative re-vealed. The new nonlocal approach developed on the basis of the nonlocal and retarded transport equations obtained within the non-equilibrium statistical physics is used to describe the occur-rence of turbulence. Within the approach, the reason for the transition to turbulence is that the non-equilibrium spatiotemporal correlation function generates the dynamic structures in the form of finite-size clusters on the mesoscale with almost identical values of macroscopic densities mov-ing as almost solid particles that can interact and rotate. The mesoparticles obtained as a result of the fragmentation of spatiotemporal correlations upon impact, move at different speeds in a me-dium with dispersion like wave packets. The movements recorded simultaneously at two scale levels indicate the energy exchange between them. Its description required a redefinition of the concept of energy far from local thermodynamic equilibrium. Experimental results show that the irreversible part of the dynamic mesostructure remains frozen into material as new defects.