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Why should equilibrium imply steady state? For example, there is a process whose rate increases with time and this process can be exactly balanced by an inverse process whose rate also increases with time.Is this not a case of non-steady state equilibrium condition?

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  • \$\begingroup\$ All my physical objections to your scenario aside, this is pure semantics: If something is increasing, you can't call it "steady" state. \$\endgroup\$ – Marcus Müller Jun 9 '18 at 13:31
  • \$\begingroup\$ I don't care what your standard study material says. Steady state requires steadiness :) \$\endgroup\$ – Marcus Müller Jun 9 '18 at 13:36
  • \$\begingroup\$ (This might simply mean that the scenario you're specifying is impossible or poorly understood: How would electrons, which don't really "exist" as particles but only as "smeared" location probability functions, move, in the same material, in opposite directions? You can't say "hey, that's 'my' electron and I can watch how it migrates" in solid state physics. Out of a false assumption, you can construct any example.) \$\endgroup\$ – Marcus Müller Jun 9 '18 at 13:40
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The question is nonsense. Electrons are completely fungible — there is no way to distinguish one electron from another.

There's no meaningful way to talk about one set of electrons flowing in one direction across an interface and a different set flowing in the other direction — all you can talk about is the net flow, which as far as I can tell, is always zero in your scenario.

So yes, in that sense, the system is in equilibrium with respect to charge.

But if the temperature is rising and electron velocities are generally increasing, then it is not in thermal equilibrium.

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To me, the semiconductor seems to be in thermal equilibrium but not in steady state which is contrary to the above statement in quotes. Please tell what is the thing I'm missing

You constructed an physically impossible example. If something is impossible, it can have any property you imagine. But it doesn't change the fact that it's wrong to derive any contradictions based on that.

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