Finite Precision Computation/Physics and Heat Energy

Euler CFD as a parameter free Theory of Everything ToE for slightly viscous incompressible fluid flow is a prime example of the idea of finite precision digital computation capable of simulating physics as a form of finite precision analog computation. Euler CFD captures turbulent flow from a principle of best possible digital solution of Euler's equations in a situation where exact (laminar) solutions are all unstable without permanence over time and so are unphysical and cannot be observed. 

The essence of turbulent flow captured by Euler CFD is the production of heat energy in turbulent dissipation from residual stabilisation in a situation where Euler residuals can be made small only in a weak mean value sense, but blow up in a strong pointwise sense. The dissipative mechanism thus expresses an impossibility to computationally resolve the flow because of finite precision, which in physical terms means production of heat energy as small scale unordered motion. 

Radiative heat transfer also involves an aspect of finite precision in the sense that a body viewed as a set of oscillators is capable of radiating only frequencies below a certain cut-off frequency scaling with temperature because synchronisation of the oscillators necessary for radiation is in finite precision impossible above cut-off. 

There is connection between turbulent flow and radiative heat transfer in that the heat energy generated in turbulent dissipation ultimately is released in radiation, and so gives a meaning to heat energy as unordered motion as unsynchronised oscillatory motion.  

Recall from the blog post 2nd Coming of the 2nd Law that finite precision computation/physics explains why certain processes are irreversible as processes where large scale kinetic energy/ordered motion is transformed into small scale kinetic energy/disordered motion, which cannot be reversed because the precision required to restore large scale order from small scale disorder is not there. This is like restoring all your manuscripts after a tornado has swept them into little pieces, or your hard disk has collapsed. 

Finite precision computation open an approach to the 2nd Law which is different from the standard based on statistics. Small scale disorder is the result of turbulent dissipation as a finite precision resolution of increasingly complex flow arising from flow instability, a resolution which cannot be reversed in finite precision.  It is like necessary (because storage is limited) chopping digits/details, which cannot be retrieved.

Heat energy as internal energy as small scale disordered motion is low quality energy in the sense that transformation to other forms of energy such as large scale motion comes with severe losses.  This puts limits to the efficiency of steam and combustion engines transforming heat energy into piston motion. On the other hand electric energy is high quality energy typically generated from large scale motion in generators allowing efficient electrical motors returning large scale motion. Heating by electricity is thus involves a form of quality degradation, which can be expensive, while heating by burning fossil fuels is efficient and cheap.