Quantum Thermodynamics of a Spin one System*

We take a collection of large non-interacting spin one particles, each having an electric dipole of
magnitude m in contact with a heat reservoir at temperature T. We apply a strong static electric
field, E Z , to the system along a z-axis causing three level split energy values. In addition to the
strong electric field, we apply a weak AC electric field in the xy-plane. This weak field induces
transitions between the three levels. Through a given protocol λ(t), the system is taken from an
initial state F(T,λ i ) to a final non-equilibrium state with parameter λ f . We analytically obtain the
expressions for the probability amplitudes for a transition from one particular initial state to the
other two final states. This will enable us to find the work distributions of a finite-time process of
taking the system from one initial state to other final states. This finite-time non-equilibrium
process will then enable us to extract equilibrium thermodynamic quantities like free energy from
non-equilibrium process, which is what we call Jarzanski equality and its relation to the second law
of thermodynamics.