# Is Information a potential or kinetic kind of energy?

It is said that the law of least action is that nature tries to convert potential energy into kinetic one as fast as possible.

Information can't be thought without a physical realisation, see here. It may be thought as a form of entropy. So information is physical and therefore it's connected to a certain kind of energy. But is it a potential or a kinetic kind of energy?

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–  draks ... Jan 8 at 23:59

## 1 Answer

Neither. Information isn't energy and can't be measured using energy units. As you pointed out, information is related to entropy which is about degrees of freedom in a system.

In physics, information is usually measured in nats but bits are common too.

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Provided a Szilard's engine a demon can extract $k_BT\ln 2$ out of 1 bit. Isn't this energy? –  draks ... Jan 8 at 23:31
@draks... no but it does take energy to change the state of a system: $E \geq \frac{\pi \hbar}{2 \Delta t}$ to change the state in $\Delta t$ time. The amount on information a system can store is related to how much energy is available. Check out arxiv.org/abs/quant-ph/9908043 for a good casual treatment of information as it relates to energy. –  Brandon Enright Jan 8 at 23:35
It's been a while since I've seen this paper. I'll reread it. +1 for bringing it back to my mind... –  draks ... Jan 8 at 23:39
Maybe my question is more philosophical: Can we measure the effort to create a mathematical theory in terms of energy? –  draks ... Jan 9 at 0:00
@draks... there is a really good book by James Gleick named The Information: A History, A Theory, A Flood which touches upon some of the history, some of the math, and some of the philosophy of information. I really enjoyed it. –  Brandon Enright Jan 9 at 0:02