### Abstract

Discrete modeling is a novel approach that uses the concept of Shannon entropy to develop thermodynamic

models that can describe fluid-phase behavior. While previous papers have focused on reviewing its theoretical background and

application to the ideal-gas model as one limiting case for fluid phases, this paper addresses its application to lattice models for

strongly interacting condensed phase systems, which constitute the other limiting case for fluids. The discrete modeling approach

is based on the discrete energy classes of a lattice system of finite size, represented by a distribution of discrete local

compositions. In this way, the model uses the same level of discretization as classical statistical thermodynamics in terms of its

partition functions, yet avoids (1) a priori averaging of local compositions by utilizing a distribution, and (2) confinement to

systems of infinite size. The subsequent formulation of the probabilities of discrete energy classes serves as the basis for

introducing the concept of Shannon information, equivalent to thermodynamic entropy, and for deriving the equilibrium

distribution of probabilities by constrained maximation of entropy. The results of the discrete model are compared to those

derived from Monte Carlo simulations and by applying the Guggenheim model of chemical theory. We point out that this

applicability of discrete modeling to systems of finite size suggests new possibilities for model development.

models that can describe fluid-phase behavior. While previous papers have focused on reviewing its theoretical background and

application to the ideal-gas model as one limiting case for fluid phases, this paper addresses its application to lattice models for

strongly interacting condensed phase systems, which constitute the other limiting case for fluids. The discrete modeling approach

is based on the discrete energy classes of a lattice system of finite size, represented by a distribution of discrete local

compositions. In this way, the model uses the same level of discretization as classical statistical thermodynamics in terms of its

partition functions, yet avoids (1) a priori averaging of local compositions by utilizing a distribution, and (2) confinement to

systems of infinite size. The subsequent formulation of the probabilities of discrete energy classes serves as the basis for

introducing the concept of Shannon information, equivalent to thermodynamic entropy, and for deriving the equilibrium

distribution of probabilities by constrained maximation of entropy. The results of the discrete model are compared to those

derived from Monte Carlo simulations and by applying the Guggenheim model of chemical theory. We point out that this

applicability of discrete modeling to systems of finite size suggests new possibilities for model development.

Original language | English |
---|---|

Pages (from-to) | 2483-2492 |

Journal | Industrial & Engineering Chemistry Research |

Volume | 55 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2 Feb 2016 |

### Keywords

- Shannon entropy
- discrete modeling
- thermodynamic modeling
- maximum entropy principle
- lattice model
- local compositions

### Fields of Expertise

- Mobility & Production

### Treatment code (Nähere Zuordnung)

- Basic - Fundamental (Grundlagenforschung)

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## Cite this

Wallek, T., Pfleger, M., & Pfennig, A. (2016). Discrete Modeling of Lattice Systems: The Concept of Shannon Entropy Applied to Strongly Interacting Systems.

*Industrial & Engineering Chemistry Research*,*55*(8), 2483-2492. https://doi.org/10.1021/acs.iecr.5b04430