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Relaxation processes in supercooled liquids are known to exhibit interestingas well as complex behavior. One of the hallmarks of this relaxation processobserved in the measured auto correlation function is occurrence of multiplesteps of relaxation. The shorter time relaxation is known as the$\beta$-relaxation which is believed to be due to the motion of particles inthe cage formed by their neighbors. One the other hand longer time relaxation,the $\alpha$-relaxation is believed to be the main relaxation process in theliquids. The timescales of these two relaxations processes dramaticallyseparate out with supercooling. In spite of decades of researches, it is stillnot clearly known how these relaxation processes are related to each other. Inthis work we show that, there is a possible universal relation between shorttime $\beta$-relaxation and the long time $\alpha$-relaxation. This relation isfound to be quite robust across many different model systems. Finally we showthat length scale obtained from the finite size scaling analysis of $\beta$timescale is same as that of length scale associated with the dynamicheterogeneity in both two and three dimensions.

Possible Universal Relation Between Short time $\beta$-relaxation and Long time $\alpha$-relaxation in Glass-forming Liquids