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Adam-Gibbs model in the density scaling regime and its implications for the configurational entropy scaling

To solve a long-standing problem of condensed matter physics with determining a proper description of the thermodynamic evolution of the time scale of molecular dynamics near the glass transition, we extend the well-known Adam-Gibbs model to describe the temperature-volume dependence of structural relaxation times, $τ_α (T,V)$. We employ the thermodynamic scaling idea reflected in the density scaling power law, $τ_α=f(T^{-1} V^{-γ} ) $, recently acknowledged as a valid unifying concept in the glass transition physics, to discriminate between physically relevant and irrelevant attempts at formulating the temperature-volume representations of the Adam-Gibbs model. As a consequence, we determine a straightforward relation between the structural relaxation time $τ_α$ and the configurational entropy $S_c$, giving evidence that also $S_c (T,V)=g(T^{-1} V^{-γ} )$ with the exponent γ that enables to scale $τ_α (T,V)$. This important finding has meaningful implications for the linkage between thermodynamics and molecular dynamics near the glass transition, because it implies that $τ_α$ can be scaled with $S_c$.