|MadSci Network: Physics|
Well, that's an interesting question because there are different ways of looking at it. "Random heat motion", as you put it, is a fundamental principle of thermodynamics and is based on a macroscopic scale. This is so because thermodynamics deals only with macroscopic variables, such as pressure, temperature, and volume. Its basic laws are expressed in terms of these quantities mentioning no such existence of atoms making up matter. However, statistical mechanics, which deals with many of the topics of thermodynamics, does suggest the existence of atoms. Now, applying the laws of mechanics statistically, one can express all the thermodynamic variables as certain averages of atomic properties. For a given macroscopic system, the number of atoms is typically so large that the averages would be very sharply defined quantities. The theory under which all this is covered is a sub-branch of the "kinetic theory of gases" called statistical mechanics, which was developed by J. Willard Gibbs (1839-1903) and by Ludwig Boltzmann (1844-1906). Thus, agitation of atoms, is not so much random, but statistical in nature. Things like probability and statistics govern how and how often atoms collide and transfer energy. Between successive collissions, a molecule in a gas will move with a constant speed along a straight line. The term "mean free path", is the average distance between these successive collisions. This mean free path is related to the density of the molecules for a given volume and to their size. Let's say we have a gas made of atoms approximated to spheres which have a diameter d. The cross section (the area of the atom presented as a target) for a collision is pi*d^2. In other words, a collision will occur when the centers of the two atoms (or molecules) are within a distance d of one another. The probability comes in when considering how often and when these collisions will occur. The reason that the word random probably comes to mind is because that so many collisions can be occuring with probabilstic results that the outcome or endpoint of any given atom/molecule at a given time for this system will be alomst impossible to predict, let alone calculate. We could follow a particulaer atom in the gas to see how hard this is to predict. The atom is travelling with a constant velocity and collides with another atom, by which an energy transfer occurs depending on the angle and initial energies. The two then fly off in their two respective directions to repeat the whole cycle. Now envision that there are several of these situations occuring and all of them interacting/overlapping at various points. The whole thing is occurring probabilistically on top of it all and would seem very easy just to label it random or chaotic. I agree with that whole-heartedly. So to summarize, I would say that the situation is chaotic, but deterministic by the laws of probability and statistics. The largest growth of statistical mechanics uses the statistical application of the laws of quantum mechanics to many-atom systems, which is called quantum statistics, rather than the application classical mechanics as is the case for statistical mechanics. In terms of pointing you to some resources or perhaps further discussion, you need only look in most physics texts (undergrad. level and up) under the heading of "kinetic theory of gases" or statistical mechanics. I performed a wide search on the WWW and had a very difficult time of locating educational materials on the subject. Perhaps some of these keywords and/or explanations will provide you with a little more insight or a new direction to take. I wish you luck and keep the questions coming if things are a little unclear.
Try the links in the MadSci Library for more information on Physics.