Residual entropy and waterlike anomalies in the repulsive one dimensional lattice gas

Abstract

The thermodynamic and kinetics of the one dimensional lattice gas with repulsive interaction is investigated using transfer matrix technique and Monte Carlo simulations. This simple model is shown to exhibit waterlike anomalies in density, thermal expansion coefficient and self diffusion. An unified description for the thermodynamic anomalies in this model is achieved based on the ground state residual entropy which appears in the model due to mixing entropy in a ground state phase transition.

Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

“…The recent interest in the study of complex systems has led to an increased focus on anomalous diffusion [4-7, 36, 42, 45], which has been described in biological systems [42][43][44], protostellar birth [47], complex fluids [48][49][50][51][52][53], electronic transportation [54][55][56][57][58][59], porous media and infiltration [60][61][62], drug delivery [63][64][65][66], fractal structures and networks [67][68][69][70][71], and in water's anomalous behavior [72][73][74], phase transitions in synchronizing oscillators [39,40,[75][76][77], to name a few.…”

The interactions between thermodynamic anomalies

“…36,[38][39][40] The flexibility to simulate a wide range of anomalous systems by changing the relative strength of two and three body terms has made the SW potential a key model for studying this behavior although soft-core potentials have also been successfully employed. [41][42][43][44][45][46][47][48][49][50][51][52] Although some of the work referenced above 29 employs methods to push the limits of metastability (by employing replica exchange techniques, for example), the anomalies in deeply supercooled regions of the phase space have not been reported in literature to date (in particular, in the low temperature limit). Related investigations, using the SW potential have studied the progression of the anomalous behavior as a function of the strength of the three body term by fitting the thermodynamic results to a two state model.…”

Estudo das anomalias da água utilizando dois modelos em rede unidimensional

“…Nosso novo modelo é similar ao descrito na seção anterior, formado por uma rede linear de comprimento L dividida em N sítios idênticos, cada um podendo estar ocupado por uma partícula ou vazio (Figura 4.9) [68]. Como o número de moléculas distribuídas na rede é igual a n, a densidade é ρ = n L .…”

“…onde h c é uma constante indêntica a entalpia local microscopia na transição de fase no estado fundamental [68]. Rescrevendo a equação 4.41 em termos das unidades reduzidas,…”

“…Em nosso segundo modelo, com uma interação puramente repulsiva, observamos os mesmos comportamentos anômalos do primeiro, contudo, desta vez com um modelo extremamente simples [68], que permitiu acessar regiões de menores temperaturas.…”