# 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 fomula 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 ?

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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.

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So the unit you are searching is kT ln2 J/bit. At room temperature (300K), this corresponds to 2.8×10⁻²¹ J/bit –  Frédéric Grosshans Nov 15 '10 at 16:25
It's incredibly tiny. In fact, our best computers generate much more heat than that when operating. –  Raskolnikov Nov 15 '10 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. –  Roy Maclean Nov 15 '10 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). –  mbq Nov 16 '10 at 9:52