# Maxwell's Demon Constant (Information-Energy equivalence)

New Scientist article: Summon a 'demon' to turn information into energy

The speed of light c converts between space and time and also appears in $E=mc^2$.

Maxwell's Demon can turn information supplied into a system into energy, which suggests there is a constant 'd' such that $E=i*f(d)$ where i is information and f is a function of d.

If d appears in the formula relating energy and information like c relates energy and mass, but c is a conversion factor between space and time, then what is d a conversion factor between?

What dimensions does d have?

Other than "Maxwell's demon constant", is there another name for d?

Or is there not a 'd' after all, instead 'c' appears once again in the information-energy equivalence formula $E=i*f(c)$?

Or is there not a constant here at all and the situation is more complicated?

Living things have evolved to exploit all kinds of opportunities - even quantum effects in the form of photosynthesis. Living things have senses to extract information from the environment, but do living cells utilise any demon effects to turn any of this information into energy ?

You're looking for this:

http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory#Information_is_physical

So, one bit of information allows an amount of work equal to $kT\ln2$. Where $k$ is Boltzmann's constant and $T$ is the thermodynamic temperature.

I've seen the article in Nature and I think it is horrible. They do a very bad service in explaining what's happening. The way they do it, it sounds like they invented a perpetuum mobile, which is not true. How was the information uncovered in the first place? That involved energy. And as thermodynamics will have it, more energy than the information provided you to perform work with the bead.

• So the unit you are searching is kT ln2 J/bit. At room temperature (300K), this corresponds to 2.8×10⁻²¹ J/bit Commented Nov 15, 2010 at 16:25
• It's incredibly tiny. In fact, our best computers generate much more heat than that when operating. Commented Nov 15, 2010 at 16:29
• I see, so in e=id, d depends on temperature, and at room.t it takes 2.8 zettabits to equal one joule. Commented Nov 15, 2010 at 17:27
• @Roy In fact it is even worse; it means that you cannot gather energy E from the thermal fluctuations unless you know at least E/(kTln2) bits of information about the system, and getting this knowledge will cost you at least E energy (in perfect conditions).
– user68
Commented Nov 16, 2010 at 9:52

To supplement, the answer for your final question. As Raskolnikov pointed out, this article lies about the fact that this process can be a source of energy, and indeed all known biological mechanisms of gathering energy satisfy energy conservation; photosynthesis gathers the energy from light and various kinds of respiration from chemical energy of various substances available in environment (that mostly also originated in photosynthesis, with exception of some esoteric ecosystems).

To ackwire information one have to spent energy. Idem to act. The Maxwell deamon or the Szilard's engine is physically (energetically) inviable.
Recently a setup was made using graphene in a solution with ions thermally (ambient) speeded that powered a LED. The ions colide with the graphene and the kinetic energy liberated stupid electrons that choose to flow in the graphene instead of neutralize the ion. This device transforms random motion in an organized flow 'a la Maxwell deamon'. It is not a free lunch.
IMO information has nothing to do with energy and I think that it can be shown that information is not constant in a closed system.