The difference between heat and work?

[muscaria]

I realize this question has arisen before in the following thread: https://www.physicsforums.com/threads/difference-between-heat-and-work.461711/ but I felt there may be more room for discussion. I feel that the nature of the effect of heat on physical systems is a rather deep one. If the flow of heat could be reduced to some kind of definite momentum transfer, there would be no need for statistical mechanics. A year ago I wrote a paper for a course I was taking and I tried to address the question somewhat. Although it is written in quantum mechanical language, the same should hold for classical systems:

"There are two different calculations which arise when considering the change in internal energy
of a system due to coupling with an external environment. Perturbing a system by transfer of heat from a heat bath gives rise to a energy change by means of a re-population to higher energy single particle states without changing the form of the Hamiltonian. On the other hand, the action of work on a system leaves the occupation of states unchanged and alters the form of the Hamiltonian, thus shifting the single particle energy levels. This is essentially the fundamental difference between work and heat: reversible work is in some sense oriented and deterministic in that it does not give rise to a reduction in knowledge of the state of the system, whereas our model for heat is undirected and inherently statistical in nature."

I had in mind that work does not change the volume of phase space of the system whereas addition of heat to the system will gradually dissipate through the system increasing the total entropy and the phase space volume will grow. In a loose sense that this jiggling of atoms is inherently unpredictable and spreads through the system. I was wondering what your guys thoughts were on this matter, is this what our picture for heat is full stop? Is there some deeper reasoning behind our statistical mechanical model? Thanks :)

 

[Philip Wood]

I think your middle paragraph holds a key insight. I remember a light starting to shine when I found it in Part I of Hill's Introduction to Statistical Thermodynamics – a masterly compact treatment. My only quibble with your middle paragraph is that perhaps it's not the form of the Hamiltonian that is altered but the values of parameters therein.

 

[muscaria]

My flatmate actually has a copy of that book, good old cheap Dover print if I recall! Should give it a check then. The middle paragraph was really only a kind of comment in the essay, which itself was on a different topic, but in it I had to go through the calculation of the response of a Fermi Liquid to an impulse magnetic field. I would have thought form was a good choice of word though given that the Work type fields couple directly to degrees of freedom of the system thus changing the form of the Hamiltonian, i.e an extra interaction term. To alter the values of parameters therein the strength of field could be varied, no?