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 electricrndipole of magnitude D in contact with a heat reservoir at temperature T . We apply arnstrong static electric field, E0, to the system along a z-axis causing three level split energyrnvalues. In addition to the strong electric field, applying a weak AC electric field inrnthe xyÀ€€plane induced transitions between the three levels. Through a given protocolrn_(t), the system is taken from an initial thermodynamic equilibrium state F(T ;_i ) to arnfinal non-equilibrium state with parameter _f . We analytically obtain the expressionsrnfor the probability amplitudes for a transition from one particular initial state to thernother two final states. This will enable us to find the work distributions of a finite-timernprocess of taking the system from one initial state to either of the two final states ofrnthe three-level system. This finite-time non-equilibrium process will then enable us tornextract equilibrium thermodynamic quantities like free energy from non-equilibriumrnprocess, which is what we call Jarzanski equality and its relation to the second law ofrnthermodynamics. We obtain the possibilities of work distributions of the three-levelrnsystem in the optimum condition for non-interacting particles. Besides, we empiricallyrnobtain the average work of the three-level system as a function of ! and timernaround the optimum frequency, where ! is the frequency of AC electric field.

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