Dear George and Fred,
George wrote: "Not sure about the application (of the general principle underlying 2nd law of TD) to the particle motion. take it more to deal with systems of particles rather than individual particle".
The above comment was with reference to my earlier statement: ...." the two processes form an interface between the two levels by usurping a fraction of energy from the lower level. The second law of thermodynamics comes into effect by way of this process of interfacing of the two levels of energy. "
This General Principle (since it is a GENERAL PRINCIPLE) should apply to particles taken separately or collectively, in the same way as gravitation applies to each an every particle in a body or the body taken as a whole.
Newton in the Principia addressed this principle. Under the 'Definitions' he dealt with both a system of particles as well as a discrete motion of a single particle (body)
About a systems of particles in motion:
"It is a property of motion, that the parts, which retain their positions to their wholes, do partake of the motions of those wholes. .... if the surrounding bodies are moved, those that are at rest within them will partake of their motion.... For the surrounding bodies stand in the like relation to the surrounded as the exterior part of a whole does to the interior, or as the shell does to the kernel; but if the shell moves, the kernel will also move, as being part of the whole, without any removal from the shell.
About the discrete motion of a particle:
"A property, near akin to the preceding is that, if a place is moved, whatever is placed therein moves along with it. THEREFORE A BODY, WHICH IS MOVED FROM A PLACE IN MOTION, PARTAKES ALSO OF THE MOTION OF ITS PLACE ...." (p. 9)
And under 'Axioms' Newton dealt with a system of particles in motion (in Corollary V) as follows: "The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forwards in a right line without any circular motion" (p. 20). ..... "A clear proof of this we have from the experiment of a ship; where all motions happen after the same manner, whether the ship is at rest, or is carried forwards in a right line...".
The above was in reference to Galileo's statement: "The CAUSE of all these correspondences of effects is the fact that the ship's MOTION IS COMMON to all the things contained in it" (p. 187).
(And do you know what this principle is? It is GALILEO'S PRINCIPLE OF RELATIVITY. Poincare removed the CAUSE - COMMON MOTION - from this principle. And used only the apparent effect to formulate his Principle of Relativity. This distortion made by Poincare is a significant contributory factor to the present crisis in Physics).
When a particle on earth is set in motion on earth, the effective applied energy p' =Mvc too HAS TO HAVE A COMPONENT OF COMMON MOTION WITH THE EARTH. And to determine this component, we need to apply EINSTEIN'S PRINCIPLE OF 'INERTIA OF ENERGY' to p'. Which is p'/c2 = Mv/c (extensive component of the energy).
As discussed in the previous post the general principle is that a fraction of energy in action is usurped equal to the product of the extensive component of the energy in action and the intensive component of the background energy field (just like in Carnot's engine). For the case of a relative motion of a particle on earth, the intensive component of the background energy is the velocity of earth's orbital motion u.
Hence the component usurped to form the organic link with the background is (Mv/c).u. Then the momentum left for relative motion is (Mv/c)(c- u).
At near light velocities v/c tends to 1. Hence for these velocities the displacement x' = (x -ut) which is the so-called "Galilean transformation".
But how do we get from here to Lorentz transformation? How do we account for the GAMMA-FACTOR in LT?
Please see the last section "Geometrodynamics of the Lorentz transformation' of my essay:.http://fqxi.org/community/forum/topic/1549
This is why Einstein INTUITIVELY wrote: "The UNIVERSAL PRINCIPLE of the special theory of relativity is contained in the postulate: The laws of physics are invariant with respect to Lorentz transformations, ..... This is a restricting principle for natural laws, comparable to the restricting principle of the non-existence of the perpetuum mobile which underlie thermodynamics" (1, p.57).
By discovering this Universal Principle (or "Top Down Causation") which runs through all the physical processes, we are proving Einstein to be right.
Best regards,
Viraj