Abstract
We revisit the equilibrium properties of a classical one-dimensional system of hardcore particles in the framework provided by the multiparticle correlation expansion of the configurational entropy. The vanishing of the cumulative contribution of more-than-two-particle correlations to the excess entropy is put in relation with the onset of a solidlike behavior at high densities.
Highlights
The entropy of a classical system can be expressed as an infinite sum of contributions associated with spatially integrated n-point density correlations: S= ∞ X Sn, (1)n=0 where S0 is the entropy of the corresponding non-interacting gas
At first sight these features may seem devoid of physical significance since in one dimension, at variance with hard disks or spheres, hard rods do not notoriously exhibit any thermodynamic phase transition to which the vanishing of the residual multiparticle entropy” (RMPE) can be possibly imputed [45]
In this paper we have revisited the equilibrium properties of the Tonks gas, a classical system of hard particles confined to one dimension, with a twofold objective: i) understanding whether it is possible to distinguish a high-density regime, with features reminiscent of the properties of a crystalline solid, from a low-density fluidlike regime, notwithstanding the absence of a conventional freezing transition; ii) verifying whether the density evolution of the so-called residual multiparticle entropy (RMPE) can be put in direct quantitative correspondence with the thermodynamic and structural behavior of the model
Summary
The entropy of a classical system can be expressed as an infinite sum of contributions associated with spatially integrated n-point density correlations: S=. Even more complex is the way in which the RMPE was found to change, as a function of the thermodynamic parameters, in a lattice gas [24, 25] of interacting positive and negative charges hosted on a two dimensional square lattice [26] This model displays a variety of both insulating and conducting phases; noteworthy is, in this case, the close correspondence between the zero-RMPE line and the (infinite-order) Kosterlitz and Thouless phase transition boundary separating the insulating-gas phase from the conducting-liquid phase. The model is frequently referred to as the “Tonks gas” after the name of one of the authors who originally derived the equation of state which was found to display no discontinuity over the entire density range aside from the expected divergence at close packing [38, 39]
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