so basically, the first time I heard about the equilibrium was on a book by ludek pachman, i believe modern chess strategy, a book by dover. he only mentions it but does not elaborate.

essentially the equilibrium is the equanimity and equal forces of the pieces in a positition which keeps everything equal.

a perfect example of a position which violates the equilibrium is the following line 1.e4 c5 2.Nf3 Nc6 3.Bb5 Na5?!-?

This move has been celebrated in certain parts of literature however it violates many principles of chess and disrupts the equilibrium. 

to appreciate it more, you can look at the line with the kibitzer on in chessbase (the engine) (i use stockfish) and it will say that white gets a +1.10 advantage after the move Na5.

Now why do I bring this up?
well essentially, you will notice that opening theory is practically, the most commonly played moves in chessbase. this makes up the mainlines in chess, the most commonly played moves in chessbase.

what you will come to realize, is that by following these lines, sometimes the lines are a + for white because the position is not being played along the equilibrium principles of piece play according to the computer. the computer is basically the leading specialist in the world in regards to the equilibrium principles.

so something that many people do is look at how the computer can improve upon these methods of play.

another thing that has been observed is that engine vs engine play leads to a ridiculous amount of draws. this happens because the computer understands how to keep the equanimity with the pieces, in other words, it doesnt often misplace pieces, and it plays more precise than any human on earth.

To come full circle, the equilibrium is one of the biggest subjects in computer chess, which is the best chess in the world.

Identifying positions where white gets a + no matter how small ( I would say +.20 or more to be more precise) from following the moves in the chessbase charts of moves (either the reference tabs, or the livebook tabs) can teach you a lot of about chess, because the computer is having a hard time meet the equilibrium demands, and states that one side has an advantage, so understanding why one side has that miniscule advantage ( a 1/4 of a pawn most of the time is what I have observed in most openings) is essential and fundamental. Now understanding how to win with that advantage becomes powerful because what you will see is that its possible with the computers, but also in human play more accordingly so, because humans are not precise.

So understanding that can turn you into a professional.