As far as I know there is no proof that the transfer of molecular kinetic energy doesn't always go from high to low as conduction.
And there is proof that kinetic energy moves in both directions.
It is called Brownian motion. I know I keep harping on it, but it is the definitive experiment and observation that proves a) the existance of molecules and atoms, b) the statistical nature of classical thermodynamics, and c) that the kinetic energy does move from the low concentration to the high concentation, just less often.
"At first the predictions of Einstein's formula were seemingly refuted by a series of experiments by Svedberg in 1906 and 1907, which gave displacements of the particles as 4 to 6 times the predicted value, and by Henri in 1908 who found displacements 3 times greater than Einstein's formula predicted.[11] But Einstein's predictions were finally confirmed in a series of experiments carried out by Chaudesaigues in 1908 and Perrin in 1909.
The confirmation of Einstein's theory constituted empirical progress for the kinetic theory of heat. In essence, Einstein showed that the motion can be predicted directly from the kinetic model of thermal equilibrium. The importance of the theory lay in the fact that it confirmed the kinetic theory's account of the second law of thermodynamics as being an essentially statistical law."
Brownian motion - Wikipedia, the free encyclopedia
The paper is available at users.physik.fu-berlin.de/~kleinert/files/eins_brownian.pdf*
This google search will provide a wealth of reading material,
https://www.google.com/webhp#q=einstein+brownian+motion
https://www.google.com/webhp#q=How+does+einstein+brownian+motion+and+heat+effect&spell=1
https://www.google.com/webhp#q=How+does+einstein+brownian+motion+and+heat
COS 126 Programming Assignment: The Atomic Nature of Matter
"In one of his "miraculous year" (1905) papers, Einstein formulated a quantitative theory of Brownian motion in an attempt to justify the "existence of atoms of definite finite size." His theory provided experimentalists with a method to count molecules with an ordinary microscope by observing their collective effect on a larger immersed particle. In 1908 Jean Baptiste Perrin used the recently invented ultramicroscope to experimentally validate Einstein's kinetic theory of Brownian motion, thereby providing the first direct evidence supporting the atomic nature of matter. For this work, Perrin won the 1926 Nobel Prize in physics. "
The bottom line of it is this. Grains of pollen are just the right size that they are visible under the microscope and small enough to be significantly impacted by the difference in momentum and kinetic energy of the individual molecules. Under a microscope, pollen grains or materal beads of sufficient size can be seen and counted as they move in random directions due to the random movement of the molecules. When they are introduced into the liquid, all at one end, they will tend towards being evenly distributed throughout the liquid. But, at any particular moment of time, a statistically calculatable quantity of beads can be seen moving in the opposite direction, in the direction of higher concentration.
This alone is sufficient to prove that statistical mechanics is correct and that classical mechanics is the result of the statistical properties of large number of atoms. And, it proves that energy does move against the temperature gradient, just not en mass.
The reason it proves it is simple. The proof of molecules and atoms proves it. The proof of atoms and molecules makes the kinetic energy of atoms and molecules sufficient to explain heat transfer. Being sufficient to explain heat transfer, having buries the caloric idea, then the gross movement of kinetic energy in opposition to the thermal gradient is proven.
One of the things with physics, and why some with never get it, is some things are understood well enough that further investigation is simply unnecessary. One could extend the brownina motion experiment to a thermal gradient experiement, but why bother?
No one with a physics education is stupid enough to think like SSDD. We all know. That he thinks otherwise is sufficient evidence to prove he doesn't have an education in engineering or physics.
Certainly the statistical evidence suggests that within any sample there will be a range of kinetic energies amoung the molecules. My point is at the scale of a single molecule. Can a lower kinetic energy molecule transfer energy to a higher energy molecule. No statistics required.
So as to not be ambiguous or misleading, the basics of Newtonian mechanics between two individual particles should be clarified.
What Newton did for science is to release it from the bonds of "why", leaving that as simply "because", and allow us to simply describe what is.
I did the derivation of momentum and energy previously, showing how F=ma, when taken over a distance or time period leads to work and momentum. (If you know this stuff, then you know this stuff. If you don't, you shoulds) It also leads to conservation of the two quantities which are simply
W=F x Δd, that is work equals force times distance (1)
KE=(1/2)mv², that is kinetic energy equals one half the mass times the velocity squared (2)
and
I=F x Δt, that is impulse equals force times time (3)
p=mv, that is momentuam equals mass times velocity. (4)
Clearly, if one objects is bouncing off another object, they experience the exact but opposite force and distance over the same period of time. That is where the conservation of momentum and energy initially comes from.
For two particles, like two pool balls, they are a system. The total energy and momentum is the same after as it was before. So,
p=m1*v1_b + m2*v2_b = m1*v1_a + m2*v2_a where a and b are after and before. (5)
E=½m1*v1_b² + ½m2*v2_b² = ½m1*v1_a² + ½m2*v2_a² (6)
m1 and m2 are the same before and after. v1_b and v2_b are what we start with.
So, we solve for eq 5 for v2_a,
v2_a=m2*v2_b-m1(v1_a-v1_b)/m2 (7)
stuff it into eq 6
½m1*v1_b² + ½m2*v2_b² = ½m1*v1_a² + ½m2*(m2*v2_b-m1(v1_a-v1_b)/m2)²
and solve that for v1_a.
m1*v1_b² + m2*v2_b² = m1*v1_a² + m2*(m2*v2_b-m1(v1_a-v1_b)/m2)²
v1_a=function(m1,m2,v1_b,v2_b)
What we get is an ugly looking equation that includes a square root and therefor has two solutions.
One of the solutions is the before that we started with {v1_b, v2_b}, leaving the other solution {v1_a, v2_a}.
Here is the thing, there is no "why". If we started with the values given by {v1_a, v2_a}, we would end up with the same pair of solutions. This is why it is said that physics mechanics is reversable with no time arrow. If two pool balls were filmed colliding and the film run backwards, it would be equally valid.
What is also notable is that, like the click clack steel ball thing, after the collision the slow ball is fast and the fast ball is slow. Do the two swap momentum and energy values or does some net momentum and energy get transfered from one to the other?
In truth, that is a philosophical question that goes towards the unanswerable question of "why". The thing is that, philosophically, there is always another why beyond the why. At some point, it doesn't matter. At some point, it is just what it is. For all we know, the reality is that there is something that is responsible for slowness, after all, the speed of light is the fixed reference, and the slowness gets transfered. It really doesn't matter.
There are a host of videos and demonstrations of this concept to be found with a search;
https://www.google.com/webhp#q=classical+mechanics+collisions
The full equation is
v1_a=(m1*v1_b+m2*v2_b)/(m1+m2) +/- (sqrt(m1*v1_b+m2*v2_b)*sqrt(m1*(v1_b-2)+m2*(v2_b-2))/(sqrt(m1)*(m1+m2)))
And, being symetrical, the 1's and 2's can be swapped around to get v2_a. This is the one dimensional case. The three dimensional case requires breaking it down to tangential and normal components which then becomes a one dimensional equation.
What doesn't happen is the slow one doesn't get slower and the fast one faster. This fact, that the slow one gets sped up and the fast one slows down, isn't the second law of thermodynamics. It seems like it, but it isn't. And this fact is only demonstrated, here, for collisions of two particles. There is an article in Wiki titled "Multi-particle collision dynamics". It is incomprehensible. For the most part, the probability of three or more particles colliding with absolute simulanaity is near impossibility. It would be interesting to know what happens, in any case. As far as I can tell, it would be two equations with three unknowns, so I'm not sure what it would yield.
When it comes to a mass of particles in a thermodynamic system, like steam or freon, the velocities are spread out. The ideal distribution is given as a Maxwell–Boltzmann distribution. This distribution, though, is not necessarily the distribution at any specific instance of time. It is the average distribution. At any specific instance of time, the velocities could be anything, as long as the total energy and momentum of the system is conserved.
Tanner's General Chemistry - Maxwell-Boltzmann Distribution Law
What the second law is saying, with the entropy tends towards maximum, is that if there are no prefered velocities and directions, then all velocities and directions will be equally represented. In a real molucular gas, like CO2, the bonds themselves will absorb kinetic energy and momentum. O-C-O leads to symetrical and asymetrical bending and stretching. Searching under "CO2 vibration modes" will yield some info. Those modes will decay to emit a photon which will then be absorbed by another molecule. And it doesn't much matter if the other molecule is sitting still or moving at a velocity. That is with the exception of relativistic effects which change the wavelength from the perspective of the molecule. So, over time, the modes become not just kinetic energy but also vibrations and photons bounding about the thermodynamic system. This is why statistical mechanics uses the vague quantity Ω(E) in S=k*ln(Ω(E)), because Ω(E) represents all the modes available at energy level E.
And this is where physics is interpreting a direction of time. Over time, the energy of the system gets spread out among all the modes that are available.