  We consider in this paper, a few important issues in non-equilibrium work
fluctuations and their relations to equilibrium free energies. First we show
that Jarzynski identity can be viewed as a cumulant expansion of work. For a
switching process which is nearly quasistatic the work distribution is sharply
peaked and Gaussian. We show analytically that dissipation given by average
work minus reversible work $W_R$, decreases when the process becomes more and
more quasistatic. Eventually, in the quasistatic reversible limit, the
dissipation vanishes. However estimate of $p$ - the probability of violation of
the second law given by the integral of the tail of the work distribution from
$-\infty$ to $W_R$, increases and takes a value of $0.5$ in the quasistatic
limit. We show this analytically employing Gaussian integrals given by error
functions and Callen-Welton theorem that relates fluctuations to dissipation in
process that is nearly quasistatic. Then we carry out Monte Carlo simulation of
non-equilibrium processes in a liquid crystal system in the presence of an
electric field and present results on reversible work, dissipation, probability
of violation of the second law and distribution of work
