• incomplete thermalization
• LGKS Markovian master equation
• non-ideal isotherm
• quantum Carnot cycle
• quantum Otto cycle

In this thesis we explore, by numerical simulation, how the finite duration of realistic
quantum cycles affects their performances. In particular we extend the concept of non-ideal
thermalization to a reasonable one of non-ideal isotherm, allowing us to precisely define the
non-ideal Carnot cycle and comparing it to the non-ideal Otto cycle.
Recently a convenient framework to treat the evolution of autonomous quadratic systems coupled
with heat baths have been established and provided that the dynamics of the system could be approximated to
be Markovian, a way of rapidly computing a two point correlation matrix at every time was found.
In our thesis such a framework is extended to treat processes where the system of interest
is coupled with its environment and some work is done on it at the same time.
Thus, to study the properties of our quantum cycles, as a working substance we have chosen a quadratic system
in such a way to drastically reduce the computation times. In particular, we have considered a
quantum Ising chain with open boundary conditions: this can be mapped into a quadratic fermionic Kitaev chain,
by means of a Jordan-Wigner transformation.
Verified that under our assumptions the non-ideal isotherm could be reproduced we give a comparison between
the work extraction efficiency of the non-ideal Otto and non-ideal Carnot cycle.