The validity of the Jarzynski equation for a very simple, exactly solvable
quantum system is analyzed. The implications of two different definitions of
work proposed in the literature are investigated. The first one derives from
measurements of the system energy at the beginning and at the end of the
process under consideration making the work a classical stochastic variable
with transition probabilities derived from quantum mechanics. In the second
definition an operator of work is introduced and the average in the Jarzynski
equation is a quantum expectation value. For the first definition a general
quantum mechanical version of the Jarzynski equation is known to hold. For the
second one the Jarzynski equation fails to yield the free energy difference at
low temperature.Comment: 5 papes, 1 figure largly rewritten and slightly enlarged versio
