In 2019, physicist Melvin Vopson of the University of Portsmouth proposed that information is equivalent to mass and energy, existing as a separate state of matter, a conjecture known as the mass-energy-information equivalence principle. This would mean that every bit of information has a finite and quantifiable mass.
So, if I invest energy in creating an ordered pattern on an abacus, it will have a different mass than a random one. Now the marbles making up the pattern stays the same. But obviously their positions wrt one another are different. The gravitational potential, however small, is different.
Is this plausible? Does an ordered abacus weigh more? Could we, in principle, weigh two identical abacusses and determine by weight which is more ordered?