  We present a unified approach to study continuous measurement based quantum
thermal machines in static as well as adiabatically driven systems. We
investigate both steady state and transient dynamics for the time-independent
case. In the adiabatically driven case, we show how measurement based
thermodynamic quantities can be attributed geometric characteristics. We also
provide the appropriate definition for heat transfer and dissipation owing to
continous measurement in the presence and absence of adiabatic driving. We
illustrate the aforementioned ideas and study the phenomena of refrigeration in
two different paradigmatic examples: a coupled quantum dot and a coupled qubit
system, both undergoing continuous measurement and slow driving. In the
time-independent case, we show that quantum coherence can improve the cooling
power of measurement based quantum refrigerators. Exclusively for the case of
coupled qubits, we consider linear as well as non-linear system-bath couplings.
We observe that non-linear coupling produces cooling effects in certain regime
where otherwise heating is expected. In the adiabatically driven case, we
observe that quantum measurement can provide significant boost to the power of
adiabatic quantum refrigerators. We also observe that the obtained boost can be
larger than the sum of power due to individual effects. The measurement based
refrigerators can have similar or better coefficient of performance (COP) in
the driven case compared to the static one in the regime where heat extraction
is maximum. Our results have potential significance for future application in
devices ranging from measurement based quantum thermal machines to
refrigeration in quantum processing networks.
