# Express bytes over cat5e as energy?

I'm interested in this purely from personal interest, I'm not a student.

Can I express 1024 bytes of information travelling over cat5e as joules (or some measure that fits into energy of e=mc^2 )? How?

Would this be radically different if it were travelling through a CPU?

I have no practical application in mind, but ideally we could express the mass of a gigabyte, and contrast it with waste from latency of an hour long transfer, or something like that. I'm sure the medium it travels over dictates a lot of this.

• A byte traveling over cat5e vs travelling through a CPU are very different things. In the CPU you are doing processing on it which requires energy to switch the transistors while over cat5e you just have the effects of the wire and the devices on each end to overcome. This will change depending on the length of the cable as well as what is on each end and what protocol you are using on the line. There isn't any value in comparing the two, especially with such broad specification. I also find it unlikely that anyone will ever be able to benefit from this question in the future. Mar 1, 2012 at 18:19

Agh .. stirrings .. Shannon ... entropy, channel capacity, information theory, agh ...

You'll be sorry :-)

Short:

The energy per bit to noise power spectral density ratio is greater than or equal to the natural logarithm of two.

Long:

Minimum energy to send k bits with and without feedback- Yury Polyanskiy, H. Vincent Poor, and Sergio Verd´

• Abstract: The question of minimum achievable energy per bit over memoryless channels has been previously addressed in the limit of number of information bits going to inﬁnity, in which case it is known that availability of noiseless feedback does not lower the minimum energy per bit. This paper analyzes the behavior of the minimum energy per bit for memoryless Gaussian channels as a function of the number of information bits. It is demonstrated that in this non-asymptotic regime, noiseless feedback leads to signiﬁcantly better energy efﬁciency. A feedback coding scheme with zero probability of block error and ﬁnite energy per bit is constructed. For both achievability and converse, the feedback coding problem is reduced to a sequential hypothesis testing problem for Brownian motion

Wikipedia - Eb/N0 - the energy per bit to noise power spectral density ratio
See section on Shannon limit.

• The Shannon–Hartley theorem says that the limit of reliable information rate (data rate exclusive of error-correcting codes) of a channel depends on bandwidth and signal-to-noise ratio according to: Where

• I is the information rate in bits per second excluding error-correcting codes;
• B is the bandwidth of the channel in hertz;
• S is the total signal power (equivalent to the carrier power C); and
• N is the total noise power in the bandwidth.

You might not expect this, but it actually depends on temperature. Basically matter always moves around with energies that are of the order of kT, where k is Boltzmann's constant and T the absolute temperature. In order to store a bit, you need to have a potential barrier that is larger than kT to prevent spontaneous changes.

Now, the exact values depend on HOW you actually design the storage (magnetic, charge, etc) but setting or resetting a bit will cost you st least kT energy.

• The OP is talking about transmitting of bits not storing of bits. Mar 1, 2012 at 18:13