If you are only confused by the "test particle," then you can think of it similarly to a multimeter. With a multimeter, you can probe a circuit to determine a voltage at one part of a circuit relative to another. With a test particle (or test charge, as I got used to hearing), you place it at a point in space, and "observe" it's behavior to see how electric (or magnetic) fields are oriented.
Like charges repel each other, so if a test charge would tend to move in a certain direction in space, then either that direction contains a negative charge (assuming you use a positive test charge), or the opposing direction contains a positive charge.
The movement of a test charge will always oppose the energy gradient (in three dimensions, energy is a scalar field, so the spatial derivatives are your forces, since energy divided by length is force). Thus, a test charge will move in the direction that achieves it's lowest energy state.
In a vacuum (such as space), ionized particles can move freely. The test charge is usually assumed to be in a state such that it can move freely. This doesn't necessarily correlate to anything real, but is a hypothetical state so the fields can be analyzed easily. You are correct in that circuits don't involve the movement of atoms or positive charges, but rather electrons (due to d-block delocalization, but that's chemistry) move. The positive charges (protons) are held in a crystalline lattice, which is why they don't move. In a conductor, electrons can move freely, so they move in response to an applied electric (or changing magnetic) field.
In free space, however, a test charge (which is really an ion, or a proton, or a positron, or a myriad of other positively charged particles) is not constrained by the bonds that hold metal atoms in place, so it can move in response to an applied field. Specifically, interactions governed by photons cause particles to exchange energy, creating the field gradient mentioned before. Therefore, test charges in free space move similarly to how electrons move in a metal (or another conductor).
While this is a convention (positive charges just seemed to be more reasonable when a lot of this math was derived), you could physically create a positively charged particle and observe it's trajectory. You could even do this at home. You'd be using a Cloud Chamber and a Beta emitter to see them.
I hope this was helpful! Let me know if you need any more clarification.
Best Answer
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´
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
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