Let's say we want to transmit information between to stations (points in space). Is there a minimal energy required to transfer a single bit of information, assuming that we tolerate that the bit might be lost or altered with a given probability?

If we want to achieve a certain bit rate (again tolerating some percentage of errors), does the required energy per bit also depend on the rate?

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    $\begingroup$ en.wikipedia.org/wiki/Landauer%27s_principle $\endgroup$ – Wolphram jonny Nov 5 '14 at 18:36
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    $\begingroup$ @julianfernandez I am not sure that "energy to transmit information" is necessarily the same as "energy lost when a bit of information is destroyed". Either that, or I don't understand Landauer's principle. $\endgroup$ – Floris Nov 5 '14 at 21:25
  • $\begingroup$ @Floris I has been a long time since I don't work on this area, so my memory might be wrong. But is one of the subjects I like. I'll try to see if I can find a good answer (I thought somebody else would answer it). I'll work on it later today. $\endgroup$ – Wolphram jonny Nov 5 '14 at 21:31
  • $\begingroup$ In the mean time, there is this rather old article ruf.rice.edu/~mobile/elec518/readings/DevicesAndCircuits/… $\endgroup$ – Wolphram jonny Nov 5 '14 at 21:37
  • $\begingroup$ There is a fantastic paper by Seth Lloyd call Ultimate physical limits to computation which addresses a very related concept and might actually answer your question. $\endgroup$ – Brandon Enright Nov 5 '14 at 22:17

The short answer to the first question is yes. You need enough power above the noise level of your systems (and space) to even receive any signal from somewhere else. You can look up articles on the Shannon-Hartley theorem, which discusses the relationship between information transfer and power, bandwidth, etc.

This is one of the most limiting factors on getting scientific data back from spacecraft. Since the power of the signal drops as $\propto$ $r^{-2}$, long distance communication with spacecraft becomes a major limitation. Spacecraft are generally powered by photovoltaic cells (i.e., solar panels) and these cells have a finite size. The spacecraft size is limited by the size of the rocket and the fairing. So all of these things are taken into account before launch.

The amount of energy than can produce is determined by the amount of sunlight they can convert, depends upon efficiency, angle of incidence, and surface area. So as a spacecraft moves further from the sun (and Earth), its capacity to generate power for a signal drops both from lower light levels and the drop in transmitter power received at Earth.

I think the answer to your second question is "kind of" or "maybe." I am not sure about this, but I do know that there are definitely minimum energy conditions in information transfer. I guess my apprehension about answering your second question is due to how you phrased it. I am not entirely sure what you are asking or looking for with that part.

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    $\begingroup$ This is a good answer for what's required in practice, but I'd also be curious about what would be required in principle, under the most ideal circumstances we can come up in a thought-experiment that doesn't violate any fundamental laws of physics (say, if the transmitter and receiver were the only objects in a perfect faraday cage that completely isolated them from external sources of electromagnetic waves). Would the nonzero ground state energy of the vacuum impose an ultimate lower bound, I wonder? $\endgroup$ – Hypnosifl Nov 5 '14 at 22:11
  • $\begingroup$ @Hypnosifl - Unfortunately, that is well beyond my area of expertise. However, quantum did teach me that practicality was more important than pure theory in some situations (ironic, no?). $\endgroup$ – honeste_vivere Nov 5 '14 at 22:16

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