Thursday, August 4, 2016

thermodynamics - 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 ?



Answer




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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