Multiple Exclusion Statistics

Abstract

A new distribution for systems of particles in equilibrium obeying exclusion of correlated states is presented following the Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the states accessible to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. The Haldane's statistics and Wu's distribution are recovered in the limit of non-correlated states of the multiple exclusion statistics. In addition, an exclusion spectrum function G(n) is introduced to account for the dependence of the state exclusion on the occupation-number n. Results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size k (k-mers) where multiple exclusion occurs. Remarkable agreement is found with Grand-Canonical Monte Carlo simulations from k=2 to 10 where multiple exclusion dominates as k increases.

Thermal hysteresis activity of antifreeze proteins: A model based on fractional statistics theory of adsorption

“…In this paper, a theoretical model to study antifreeze protein adsorption to ice and thermal hysteresis activity has been presented. The new scheme combines (i) the argument of Burcham et al [14], which indicates that the thermal hysteresis activity depends linearly on the fraction of ice surface occupied by AFPs; and (ii) the fractional theory of adsorption [31,32], where the struc-…”

“…According to Appendix A, the ratio Θ/Θ m can be expressed as the fraction of ice surface occupied by AFP molecules θ = Θ/Θ m [Eq. (A.20)], and θ can be calculated on the base of the fractional statistics thermodynamic theory of adsorption [30][31][32]. Fractional approximation provides a general theoretical scheme to model the adsorption of structured molecules.…”

“…In line with previous work [14,[27][28][29], a model in two dimensions to study the adsorption of AFPs of different shapes and sizes on ice substrates is introduced in the present article. The theoretical scheme is based on the fractional statistics formalism [30][31][32]. The corresponding thermodynamic functions are analytically developed.…”

Fractal-Like Kinetics of Adsorption Applied to the Solid/Solution Interface

“…More recently, a new distribution for systems of particles in equilibrium obeying the exclusion of correlated states was introduced following Haldane's state counting. 17 Knowledge of kinetic features in a solid/solution system provides an insight into the possible mechanism of adsorption along with the reaction pathways. 18 Several kinetic models have been used to predict the adsorption kinetics in solid/ solution interfaces.…”

“…Recently, Riccardo et al presented a new theoretical description of the fractional statistical theory of adsorption phenomena based on Haldane’s statistics for complex adsorption systems. More recently, a new distribution for systems of particles in equilibrium obeying the exclusion of correlated states was introduced following Haldane’s state counting …”