02481nas a2200241   4500008004100000022001400041245016600055210006900221260000900290300001100299490000800310520158300318100002501901700001701926700001501943700002401958700002501982700002302007700002202030700002202052700003402074856013102108       2022                        eng d  a0021-960600aThermodynamics and its correlation with dynamics in a mean-field model and pinned systems: a comparative study using two different methods of entropy calculation0 aThermodynamics and its correlation with dynamics in a meanfield   cJAN   a0145030 v1563 aA recent study introduced a novel mean-field model system where each particle over and above the interaction with its regular neighbors interacts with k extra pseudo-neighbors. Here, we present an extensive study of thermodynamics and its correlation with the dynamics of this system. We surprisingly find that the well-known thermodynamic integration (TI) method of calculating the entropy provides unphysical results. It predicts vanishing of the configurational entropy at temperatures close to the onset temperature of the system and negative values of the configurational entropy at lower temperatures. Interestingly, well below the temperature at which the configurational entropy vanishes, both the collective and the single-particle dynamics of the system show complete relaxation. Negative values of the configurational entropy are unphysical, and complete relaxation when the configurational entropy is zero violates the prediction of the random first-order transition theory (RFOT). However, the entropy calculated using the two-phase thermodynamics (2PT) method remains positive at all temperatures for which we can equilibrate the system, and its values are consistent with RFOT predictions. We find that with an increase in k, the difference in the entropy computed using the two methods increases. A similar effect is also observed for a system where a randomly selected fraction of the particles are pinned in their positions in the equilibrated liquid. We show that the difference in entropy calculated via the 2PT and TI methods increases with pinning density.1 aNandi, Ujjwal, Kumar1 aPatel, Palak1 aMoid, Mohd1 aNandi, Manoj, Kumar1 aSengupta, Shiladitya1 aKarmakar, Smarajit1 aMaiti, Prabal, K.1 aDasgupta, Chandan1 aBhattacharyya, Sarika, Maitra  uhttps://library.ncl.res.in/content/thermodynamics-and-its-correlation-dynamics-mean-field-model-and-pinned-systems-comparative