Express bytes over cat5e as energy?
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.





Useful Wikipedia - Entropy in thermodynamics and information theory

Also  Shannon’s Channel Capacity and BER 
Notes on Shannon’s Limi

and Shannon's Channel Capacity