## Internal components of continuous quantum thermal machines.

##### Author

González López, Javier Onam##### Date

2019##### Abstract

The dynamics of continuous quantum machines weakly coupled to thermal
reservoirs is described by master equations when the bath temperatures are
high enough. If, in addition, the bare frequency gaps are much larger than
the thermal couplings, the steady state or limit cycle of the device coincides
with the stationary solution of a set of balance equations. This solution can
be analyzed by using Graph Theory. Within this framework, the balance
equations are represented by a graph. We employ a circuit decomposition
of this graph to calculate and, most importantly, interpret the stationary
thermodynamic properties of different continuous devices. We show that each
circuit can be associated with a thermodynamically consistent mechanism.
This follows from the consistency of the corresponding master equations with
the Laws of Thermodynamics for a proper definition of the energy currents.
As a consequence, these circuits can be thought of as internal components
of the corresponding machine. Thus, the overall steady state functioning of
the device is the result of the contributions of its internal components and
the interplay between them.
We study two types of continuous devices. On one hand, we analyze ab-
sorption machines including only thermal baths. We show here that not only
the total number of constituents circuits affects the device performance, but
also the specific structure of the graph containing these circuits. Crucially,
we find that the device connectivity has a major role in the design of optimal
absorption machines. On the other hand, we consider periodically driven
devices with a cyclic pattern of transitions. These machines are connected
to thermal baths and also to a sinusoidal laser field. We study both the
strong and the weak driving limits by using Global and Local master equa-
tions respectively. We compare these approaches with the Redfield master
equation. A circuit decomposition can be used to describe the stationary
thermodynamic quantities in both limits. Interestingly, given an arbitrary
basis, the device needs coherences to operate in the weak driving limit. How-
ever, an incoherent stochastic-thermodynamic model may replicate the same
stationary functioning.
We conclude that the steady state thermodynamic operation in all the
models under consideration can be described without invoking any quantum
feature. Along these lines, the graph approach may be useful for identify-
ing genuinely quantum effects in other continuous machines. For example,
devices with non-cyclic pattern of transitions and degenerate states.