# Is there a lower bound on energy needed to transfer one bit of information?

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?

• en.wikipedia.org/wiki/Landauer%27s_principle – Wolphram jonny Nov 5 '14 at 18:36
• @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. – Floris Nov 5 '14 at 21:25
• @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. – Wolphram jonny Nov 5 '14 at 21:31
• In the mean time, there is this rather old article ruf.rice.edu/~mobile/elec518/readings/DevicesAndCircuits/… – Wolphram jonny Nov 5 '14 at 21:37
• 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. – Brandon Enright Nov 5 '14 at 22:17

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.