In the last part of the third paragraph of the above article it says:

"In fact, Szilárd formulated an equivalence between energy and information, calculating that kTln2 (or about 0.69 kT) is both the minimum amount of work needed to store one bit of binary information and the maximum that is liberated when this bit is erased, where k is Boltzmann's constant and T is the temperature of the storage medium. "

Now, I find this connection between energy and information rather odd for the following reason: Consider two computational systems, each made of buckets of water, with the only difference between the two being the size of the buckets. That is, system A consists of 10 liter buckets while system B consists of 1 liter buckets. It seems evident that the amount of work done to perform a computation in system A would be a lot more than the amount of work done to perform the same computation on system B. My main point from this analogy is that energy required to store or manipulate bits of information seems to be technology-dependent. Can someone come up with the weakness in my analogy or provide a better analogy that could explain how the energy-information equivalence is valid? (I have only a rudimentary understanding of the concept of information).

  • $\begingroup$ note that the cost is in energy erasure $\endgroup$ Sep 26, 2012 at 21:09
  • $\begingroup$ Check out Landauer's principle. $\endgroup$
    – tparker
    Sep 28, 2016 at 20:49
  • $\begingroup$ I should clarify that the kind of computational device that I'm referring to is something akin to a mechanical contraption that empties and fills different buckets of water, where a full bucket implies a "1" and an empty bucket implies a "0". $\endgroup$
    – Joebevo
    Oct 21, 2018 at 4:39

1 Answer 1


The information isn't stored in the bucket, it's stored in a device which is exchanging thermal energy with the bucket, like a ball in one of two minima in a cup. You need to move the ball between the minima to write the information, and to make this store data, you need to reduce the phase space volume of the ball plus water by a factor of 2, which gives the bound you are talking about. The phase space volume is the definition of entropy. The relation is not there at zero temperature, you can store bits with arbitrarily small amounts of energy then.


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