Elaboration of Wolfram's Explanation of the Second Law

da Vinci's explanation of the 2nd Law = Mine.

Stephen Wolfram is now presenting work on the 2nd Law of Thermodynamics based on the notion of computation, which connects to a view I have been advocating. The role the 2nd Law is to give an explanation in mathematical terms of the observed fact that certain macroscopical physical processes are irreversible even though the underlying microscopics based on Newton's Laws appears to be reversible. 

Boltzmann tried to give an explanation in terms of statistics, which has not convinced Wolfram nor me, since we have both tried to replace statistics by computation as a process taking a system from one configuration at a certain time $t$ to a next configuration at $t+dt$ with $dt$ a small time step.  My theory is presented in the books Computational Turbulent Incompressible Flow and Computational Thermodynamics with Johan Hoffman and blog posts.

I will not here seek to summarise Wolfram's theory, which he admits is not easy to fathom, but just briefly recall the elements of my theory which is different by qualifying the general idea of computation in terms of the concepts of (i) finite precision computation and (ii) stability/well-posedness (connecting to Wolfram's computational irreducibility).

The phenomenon of turbulence of fluid motion demonstrates the role of (i) and (ii) in explaining why certain processes are not reversible. The basic feature of turbulent flow is that it contains a range of scales from large to small with large carrying kinetic energy in ordered coherent form and small carrying heat energy as unordered incoherent form. 

Fluid flow may be seen as initiated in large scale coherent form like the laminar flow in a river before a water fall in which it transforms into small scale turbulent flow by the fall developing strong velocity gradients, see picture above. In the fall coherent laminar flow develops into turbulent flow thus transforming large scale coherent kinetic energy into small scale incoherent heat energy. 

This is a stable process in the sense that the large scales and amount of heat energy will change little under finite precision of the computational process over a time. In other words, the large scale forward process is stable or well-posed. It is possible to break down large scale kinetic motion into small scale heat energy with only finite precision = Easy. You can easily break a glass by a hammer without much precision.

On the other, reversing the flow through the water fall is impossible, because it would require infinite precision to coordinate incoherent small scale turbulent flow/heat energy into large scale laminar flow /kinetic energy = Difficult. To assemble a glass smashed into pieces is difficult/impossible. 

Digital computation has finite precision. We do not have to ask physical processes to be carried out by some form of computation with infinite precision; finite precision is enough.  

Summary of Irreversibity/2nd Law: 

• Forward motion in time is possible/easy under finite precision: physics. 
• Backward motion in time is impossible/difficult under finite precision: not physics.          

PS1 Wolfram gives a (human) observer with certain perception capabilities a key role, like in the Copenhagen interpretation of quantum mechanics. But a Universe without observer is also a Universe maybe of more fundamental interest. 

PS2  There is a connection to both previous and next post describing turbulent flow as predictable chaotic and irreversible flow.