Finite-time thermodynamic processes of a spin-one quantum electric dipole system

We take a collection of large non-interacting spin one particles, each having an electric dipole of magnitude, D, in contact with a heat reservoir at temperature T. We apply a strong static electric field, E₀, to the system along a z-axis causing three level split energy values. In addition to the strong electric field, applying a weak AC electric field in the xy−plane inducedes transitions between the three levels. Through a given protocol,ζ(t), the system is taken from an initial thermodynamic equilibrium state F(T,τ_i) to a final non-equilibrium state with parameter ζ_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 either of the two final states of the three-level system. This finite-time non-equilibrium process will then enable us to extract equilibrium thermodynamic quantities like free energy from non-equilibrium process. We empirically obtain the average work of the three-level system as afunction of the frequency of AC electric field and time around the optimum frequency.