We know that the noise from a resistor in thermal equilibrium cannot heat up another resistor, even if you connect them via an electrical isolator. This is the Second Law of thermodynamics.
But the question is to explain what is going on in microscopic detail. How does the system in fact maintain balance?
Just for reflection; I am not a physicist, but the system described is reminescent of the case of osmosis in which a semi-permeable membrance divides two solutions containing solutes A and B, only one of which is able to traverse the membrane....an equilibrium is attained that involves an osmotic pressure, the flow of the permitted solute towards equilbrium and a decrease in entropy. The exact mechanism on a molecular scale is not resolved, from the frame of the membrane and solutes the osmotic effect is reversible and can be driven backwards...the desalination of seawater has been demonstrated. Absent from description is whole frame involving "universe" in which work accomplished entails an increase in entropy. I think the system of particles and mathematics described is further than 'ideal' along the trail from laws about particulars towards a real universe...the insolator cannot really be considered isolated and measurement across the insolator entails change, however incremental to the external cosmos. For engineering purposes this may not be important though entailed philosophically is a potentail to induce universal change with the application of high energy to small volumes...similarly within access is a comprehendable ethic to use as a guide to understand what is practical to endeavor in the pursuit of basic research question and theory.
to add: some researchers claim that high energy particle accelerators create black holes....or that microwaves cause cancer...there are probably many potential effects from sequestration and applied impulse in experiement as well as in technological application. I did not mean to change the topic but the answer to questions may entail it.
@Kai. An optical isolator contains a material that rotates polarization by 45 deg. Then if you put polarizers either side, at 45 deg, you have an isolator. So in one direction some light is absorbed by the first polariser, but passes the second polarizer. On the return trip light is absorbed by both polarizers. This device is called a Faraday isolator.
Anyhow, that was not the question! The question is what happens in an electrical isolator :-)
In my understanding an electrical isolator switches off, isolates, the conduction of electrons. The conduction of electrons, flow of electons, stops at the time the isolator is activated. If the resistors are at thermal equilibrium at the time of isolation the second law is maintained and entropy has reached it maximum state for the system.
The electrical isolator has determined an isolated system in which no free electrons are moving or escaping or excited beyond the ground state, the resistors are in equilibrium. Given the system is an isolated system in thermodynamic equilibrium, each and every microstate is equally probable (fundamental assumption of statistical mechanics). With electrical isolation the system is no longer 'energized', a potential difference in voltage is not present nor inroduced and the microstates are in their ground state of equilibrium.
Visualizing the microstates of the resistors, at this isolated equilibrium state, would we not see stable non-excited molecular configurations, assuming 'seeing' does not entail introducing energy sources (photons, electrons, etc) that would violate the condition of an electrical isolator?
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