  We present a self contained formalism modelled after the Brownian motion of a
quantum harmonic oscillator for describing the performance of microscopic
Brownian heat engines like Carnot, Stirling and Otto engines. Our theory,
besides reproducing the standard thermodynamics results in the steady state
enables permits us to study the role dissipation plays in determining the
efficiency of Brownian heat engines under actual laboratory conditions. In
particular, we analyse in detail the dynamics associated with decoupling a
system in equilibrium with one bath and recoupling it to another bath and
obtain exact analytical results which are shown to have significant
ramifications on the efficiencies of engines involving such a step. We also
develop a simple yet powerful technique for computing corrections to the steady
state results arising from finite operation time and use it to arrive at the
thermodynamic complementarity relations for various operating conditions and
also to compute the efficiencies of the three engines cited above at maximum
power. Some of the methods and techniques and exactly solvable models presented
here are interesting in their own right and, in our opinion, would find useful
applications in other contexts as well.
