Physical 2nd Law Without Statistics and Entropy

Why is there a 2nd Law of Thermodynamics?

In the book Computational Thermodynamics a 2nd Law of Thermodynamics is formulated as follows in the setting of Euler's equations for a compressible fluid/gas with vanishing viscosity (with quantities integrated in space): 

• $\frac{dK}{dt} - W=Q\ge 0$,               (2nd Law)

where $K$ is kinetic energy, $W$ is mechanical work of variable sign (positive in expansion) and $Q>0$ is turbulent dissipation as a positive quantity adding to internal heat energy. In this formulation all quantities involved have physical meaning and no notion of entropy of unclear physical meaning is present (and so is not needed). Neither is any statistics involved. 

The 2nd Law states a limit to transformation between kinetic energy and work with turbulent dissipation appearing as a loss in the form of heat energy, which according to a stability analysis in the book, always is present locally in space and time. The loss is thus inevitable. The loss is also irreversible, since time reversal violates the sign of (2nd Law) and so gives an arrow of time. Kinetic energy once converted to heat energy cannot be retrieved as an expression of the term internal energy. 

The above formulation of the 2nd Law closely connects to classical formulations preceding that of Boltzmann, who introduced statistics and entropy. A new aspect is that it is based on Euler's equations as a precise mathematical model, in particular on computational solution in a certain precise weak-strong sense reflecting that strong solutions do not exist. This gives the 2nd Law a precise computational mathematical meaning in the presence of finite precision, which can be interpreted in physical terms so can be referred to as a Physical 2nd Law. 

The reason that heat energy as micro-scale unordered kinetic energy once created in turbulent dissipation, cannot be retrieved into macro -cale ordered kinetic energy, is that it requires a very high precision which cannot be met with finite precision physics/computation.  

The Physical 2nd Law thus appears as a resolution in the digital age of a basic problem of physics, which could not be resolved within classical analytical mathematics nor statistics. 

This post connects to earlier posts on Wolfram's recently presented resolution also based on computation but in fundamentally different form. 

Modern physicists have since long left the 2nd Law behind as a trivial no-problem not asking for any resolution although it has been an outstanding open problem of physics, and have so proceeded to new orchards of string theory and multi-versa, which however have not delivered any fruits and so a return to basics could possibly be of some interest to todays fundamental physicists, or not?