  We consider a simple model of a stochastic heat engine, which consists of a
single Brownian particle moving in a one-dimensional periodically breathing
harmonic potential. Overdamped limit is assumed. Expressions of second moments
(variances and covariances ) of heat and work are obtained in the form of
integrals, whose integrands contain functions satisfying certain differential
equations. The results in the quasi-static limit are simple functions of
temperatures of hot and cold thermal baths. The coefficient of variation of the
work is suggested to give an approximate probability for the work to exceeds a
certain threshold. During derivation, we get the expression of the
cumulant-generating function.
