So, I was working on a problem and I thought if it is always possible to split the Hamiltonian of a closed system into two parts, one containing non-interacting constituents and the other consisting of the energy of the force carriers. These two systems will be at equilibrium by themselves but not in equilibrium with each other. The thermodynamic macroscopic variables will then have contribution from both the sub-systems.
Separating H into H0 (non-interacting, static) + H'(interacting) is a normal practice in quantum mechanics as "perturbation theory".
Two systems at equilibrium by themselves, if not interacting with each other, will stay at equilbrium separately by themselves. Any macroscopic 'extensive' variable would be the summation of the two systems.
Two systems, if interacting with each other and not in equilibrium with each other, will not be able to main their equilibrium until the entire system reaches equilibrium.Enegy is conserved according to the first law of thermodynamics.
Sir i was thinking of breaking the hamiltonian of a gas of charged particles into two parts.
1. Hamiltonian of Free particle
2. The hamiltonian of the coulomb force carriers.
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