# Is it possible to calculate the information content of matter? How?

I know the Bekestein bound is the upper bound for the information content of a region of space, but is it possible to actually calculate that information content (number of bits, not the bits themselves)?

For example, given 1mL of water at room temperature, I can say its energy is MC^2 (mass-energy equivalence) + HTM (heat capacity * temperature * mass, its thermal energy) / kTln2 (Landauer's principle, joules per bit of information entropy). Does this mean that 1mL of water contains 3.13 * 10^34 bits of information, or is this misguided of me to think?

1mL of water is only 3.34 * 10^22 molecules, based on the molarity, so the 3.13E34 number seems very high to me...

• The mc^2 at the thermodynamic level is irrelevant since most of that energy is bound in the nucleus, (a tiny bit in the atoms and molecules). Thermodynamic entropy does not know about mc^2 in these terms. – anna v Mar 20 '15 at 4:56
• Point taken, but without the MC^2 term, the result only describes the number of bits of information potentially able for doing thermodynamic work and not all of the information contained in the matter, correct? – haydnv Mar 23 '15 at 3:44

• But still, your suggested form of (MC^2) / kTln2 would give exactly the same result for, i.e., 1g of water at 300K and 1g of hydrogen gas at 300K and 1g of solid gold at 300K, yes? How can that be? Isn't the free energy very different in those forms and isn't that potentially an information-bearing degree of freedom? – haydnv Mar 23 '15 at 3:50