This assignment has two parts.
First, complete the
following calculation. Consider
a very simple model of a
computer memory in which molecules are either found to reside
in the left half
of their memory cell (encoding a “0”), or in the right half
(encoding a "1"). Imagine
that
we have a 10-bit register.
Initially each cell is in the "0" state (i.e., all 10 particles are in the left side of
their respective
cells). After the
computation, they
are in either half of the cell (depending on the specific
computation). This
doesn't necessarily require any work.
For example, if one simply pulls out the dividing wall
between the
"0" and "1" side, the particles can by free expansion move
from the "0" state into the "1" state.
Your task is to determine the energy cost
to reset the
10-bit register to its initial state, where every particle is
again in the
"0" side of its cell.
This can be done by using a piston to push the
particles (~compressing
the gas) so that they can only occupy the left side of the
cell. Here are
the two relevant questions for
you to answer (for both of them, assume the Temperature is
constant, at T):
1. What is the change in dimensionless
entropy during this
process?
2. What energy is required to carry out the process?
Then, read
the extremely interesting article SciAmDemons-Bennett
(find it here),
which links thermodynamics to information theory, and write a
1-2 page essay on
it in which you:
a. Summarize the problem of Maxwell's demon
b. Summarize the several incorrect solutions to this paradox
c. Explain the correct solution
d. Finally, explain the connection between this topic and that
of
"reversible computing" (which you should research a little).