We analyzed Solar Dynamics Observatory line-of-sight magnetograms for a decaying NOAA active region (AR) 11451 along with co-temporal Extreme-Ultraviolet Imaging Spectrometer (EIS) data from the Hinode spacecraft. The photosphere was studied via time variations of the turbulent magnetic diffusivity coefficient, η(t), and the magnetic power spectrum index, α, through analysis of magnetogram data from the Helioseismic and Magnetic Imager (HMI). These measure the intensity of the random motions of magnetic elements and the state of turbulence of the magnetic field, respectively. The time changes of the non-thermal energy release in the corona was explored via histogram analysis of the non-thermal velocity, vnt, in order to highlight the largest values at each time, which may indicate an increase in energy release in the corona. We used the 10% upper range of the histogram of vnt (which we called Vuppnt) of the coronal spectral line of Fe xii 195 Å. A 2 day time interval was analyzed from HMI data, along with the EIS data for the same field of view. Our main findings are the following. (1) The magnetic turbulent diffusion coefficient, η(t), precedes the upper range of the vnt with the time lag of approximately 2 hr and the cross-correlation coefficient of 0.76. (2) The power-law index, α, of the magnetic power spectrum precedes Vuppnt with a time lag of approximately 3 hr and the cross-correlation coefficient of 0.5. The data show that the magnetic flux dispersal in the photosphere is relevant to non-thermal energy release dynamics in the above corona. The results are consistent with the nanoflare mechanism of the coronal heating, due to the time lags being consistent with the process of heating and cooling the loops heated by nanoflares.
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