The Superfluid High REynolds von Kármán experiment (SHREK) has been designed to study the fundamental characteristics of turbulence at very high Reynolds number flows using a medium of normal helium (HeI) or superfluid helium (HeII). The velocity fluctuations were measured by the technique of hot-wire anemometry in classical liquid helium at T = 2.2K and P = 3bar. The dimensionless dissipated power per unit mass estimated from the hot-wire measurements has found to reach an asymptotic value with respect to Reynolds number for each of the configuration of von Kármán flow. The turbulence cascade is one of the non-equilibrium thermodynamic process, which can be expressed by solving the Fokker-Planck equation (FPE) using the experimental hot-wire data. Using the solution of FPE in terms of drift and diffusion coefficient, the total entropy change Stot is estimated from the system entropy change Ssys and the medium entropy change Smed for each of the turbulence cascade trajectory starting from integral length scale L down to Taylor microscale λ. The validity of the integral fluctuation theorem is proved. Experimentally, the validity of the increase of entropy principle is addressed for the SHREK experimental data with respect to Reλ up to O(104)