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We propose a novel method to construct the Landau thermodynamic potentialdirectly from the fluctuations measured in heavy-ion collisions. The potentialis capable of revealing the signal of the critical end-point (CEP) and thefirst order phase transition (FOPT) of QCD in the system even away from thephase transition region. With the available experimental data, we show that thecriterion of the FOPT is negative for most of the collision energies whichindicates no signal of FOPT. The data at $\sqrt{s_\mathrm{NN}}=7.7$ GeV with0-5% centrality shows a different behavior and the mean value of the datasatisfies the criterion. However, the uncertainty is still too large to make acertain conclusion. The higher order fluctuations are also required forconfirming the signal. We emphasize therefore that new measurements with higherprecision for the $C_{1,...,6}$ within 0-5% centrality in the vicinity of$\sqrt{s_\mathrm{NN}}=7.7$ GeV are in demand which may finally reveal thesignal of QCD phase transition.

Revealing the Signal of QCD Phase Transition in Heavy-Ion Collisions