The state of thermodynamic equilibrium is typically defined referring to the system's behaviour in the future. Can the definition be formulated in terms of measurable quantities?
Technically, a system is in thermodynamic equilibrium if:
Every part of the system has a well-defined temperature. For example:
- If there's an ideal gas, the velocities satisfy the Maxwell-Boltzmann distribution (for some temperature);
- If there are photons, their intensity and spectrum satisfies the blackbody radiation formula (for some temperature)
- If there are chemical bonds breaking and re-forming, the higher-energy configurations occur less often, exactly following the Boltzmann distribution (for some temperature)
- etc. etc.
All of those temperatures of all of those components are exactly the same.
I guess I could have just said "It satisfies the Boltzmann distribution, for some fixed temperature". The above is just a roundabout way to say that. But I wanted to be more specific. :-D
**Footnote: In practice, people refer to a system as being in thermodynamic equilibrium even if some degrees of freedom (i.e., ways to store energy) do not satisfy the Boltzmann distribution ... as long as those degrees of freedom can only change so very very slowly that we can treat it as being stuck in its configuration "forever". A stupid example is nuclear degrees of freedom: According to the Boltzmann distribution, hydrogen atoms should fuse together into helium. But that will only happen if you wait 100 grillion gazillion years, or if we're talking about stars or nuclear weapons. So we freely refer to systems as being in thermodynamic equilibrium even if they have hydrogen atoms in them. That's an extreme example. There are many more murky examples. Is my refrigerator in thermodynamic equilibrium, even though the cheese is gradually going bad (undergoing slow chemical reactions)? Not really but yes for some purposes.