"equilibrium to" is correct and usable in written English.
You can use this phrase to indicate that two (or more) entities are equally balanced. For example, "We worked to restore equilibrium to the market prices."
What brought Kenya's equilibrium to an end?
Jarrett attributes Obama's equilibrium to his upbringing.
Mr Selten extended the Nash equilibrium to such settings.
We must bring greater equilibrium to our policy in the region.
For others, smoking is an old friend, a pacifier that adds equilibrium to these uncertain times.
Perhaps the United States' more vigorous economy allowed the plutocratic equilibrium to survive.
His writing is earthed and ethereal – there is a rare equilibrium to it.
"The emergency order temporarily banning short selling of financial stocks will restore equilibrium to markets".
She envisages arriving at an equilibrium to compare with water's, balancing "the weight of hope against the light of patience".
Instead, it will take a force of magnanimity and graciousness to restore equilibrium to nation and individuals.
There's no straightforward calculation that will yield the ideal policy for shifting an economy from a "bad" equilibrium to a "good" one.
