  We compute the average work done by an external agent, driving a piston at
constant speed, over a single particle gas going through an adiabatic
compression and expansion process. To do so, we get the analytical expression
relating the number of collisions between the piston and the particle with the
position of the piston during the process. The ergodicity breaking of the
system during the process is identified as the source of its irreversibility.
In addition, we observe that by using particular initial distributions for the
state of the particle, it is possible to preclude the possibility of a net
energy transfer from the agent to the particle during the process.

Classical Physics