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Mathematical description of light-induced DL as a probability distribution

HK Hong Bae Kim
KB Ku Youn Baik
PC Pill-Hoon Choung
JC Jong Hoon Chung
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The relaxation of a non-equilibrium state into the equilibrium of a complex system can be approximated by a power law34. The DL temporal trend for a biological system can be modeled by a hyperbolic function, as given in ref.35:

where I(t) is the emitted intensity that can be obtained from the experimental data, I 0 is the initial value of the emitted intensity, t is time, and t 0 is an initial value.

DL intensity, I(t), is associated through the decay probability, P(t), with the degree of excitation, n(t), that attenuates at any time t by the expression I(t) = −dn(t)/dt 34. This can be evaluated for the value of a dimensionless function obtained from the experimental values of the intensity, I(t), at a time t, as follows34:

where

Using the data from Fig. 2, P(t) and n(t) are obtained.

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