Nonequilibrium thermodynamics for a harmonic potential moving in time

We investigate non-equilibrium thermodynamics externally driven by moving the center of harmonic potential in time. We present the theoretical formalism for an arbitrary motion in underdamped dynamics. We provide the formulas to find thermodynamic quantities such as work, heat and entropy production produced for time period, which are main quantities in non-equilibrium studies. For sinusoidal driving with external frequency Ω, we observe a resonance for work production where the average rate for infinite period is maximized at Ω=ω0that is the internal frequency of the harmonic oscillator. It may be used for an alternative way to measure the stiffness of an optical trap potential. We confirm the thermodynamic uncertainty relation newly found for underdamped dynamics subject to general time-dependent protocols for a specific example of driving.