Discrete Modeling of Lattice Systems: The Concept of Shannon Entropy Applied to Strongly Interacting Systems

Thomas Wallek, Martin Pfleger, Andreas Pfennig

Research output: Contribution to journalArticleResearchpeer-review

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.
Original languageEnglish
Pages (from-to)2483-2492
JournalIndustrial & engineering chemistry research
Volume55
Issue number8
DOIs
Publication statusPublished - 2 Feb 2016

Fingerprint

Entropy
Fluids
Statistical mechanics
Phase behavior
Gases
Thermodynamics
Chemical analysis

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)

Cite this

Discrete Modeling of Lattice Systems: The Concept of Shannon Entropy Applied to Strongly Interacting Systems. / Wallek, Thomas; Pfleger, Martin; Pfennig, Andreas.

In: Industrial & engineering chemistry research, Vol. 55, No. 8, 02.02.2016, p. 2483-2492.

Research output: Contribution to journalArticleResearchpeer-review

@article{70db02b796ce49b2888fae2eb45c9f77,
title = "Discrete Modeling of Lattice Systems: The Concept of Shannon Entropy Applied to Strongly Interacting Systems",
abstract = "Discrete modeling is a novel approach that uses the concept of Shannon entropy to develop thermodynamicmodels that can describe fluid-phase behavior. While previous papers have focused on reviewing its theoretical background andapplication to the ideal-gas model as one limiting case for fluid phases, this paper addresses its application to lattice models forstrongly interacting condensed phase systems, which constitute the other limiting case for fluids. The discrete modeling approachis based on the discrete energy classes of a lattice system of finite size, represented by a distribution of discrete localcompositions. In this way, the model uses the same level of discretization as classical statistical thermodynamics in terms of itspartition functions, yet avoids (1) a priori averaging of local compositions by utilizing a distribution, and (2) confinement tosystems of infinite size. The subsequent formulation of the probabilities of discrete energy classes serves as the basis forintroducing the concept of Shannon information, equivalent to thermodynamic entropy, and for deriving the equilibriumdistribution of probabilities by constrained maximation of entropy. The results of the discrete model are compared to thosederived from Monte Carlo simulations and by applying the Guggenheim model of chemical theory. We point out that thisapplicability of discrete modeling to systems of finite size suggests new possibilities for model development.",
keywords = "Shannon entropy, discrete modeling, thermodynamic modeling, maximum entropy principle, lattice model, local compositions",
author = "Thomas Wallek and Martin Pfleger and Andreas Pfennig",
year = "2016",
month = "2",
day = "2",
doi = "10.1021/acs.iecr.5b04430",
language = "English",
volume = "55",
pages = "2483--2492",
journal = "Industrial & engineering chemistry research",
issn = "0888-5885",
publisher = "American Chemical Society",
number = "8",

}

TY - JOUR

T1 - Discrete Modeling of Lattice Systems: The Concept of Shannon Entropy Applied to Strongly Interacting Systems

AU - Wallek, Thomas

AU - Pfleger, Martin

AU - Pfennig, Andreas

PY - 2016/2/2

Y1 - 2016/2/2

N2 - Discrete modeling is a novel approach that uses the concept of Shannon entropy to develop thermodynamicmodels that can describe fluid-phase behavior. While previous papers have focused on reviewing its theoretical background andapplication to the ideal-gas model as one limiting case for fluid phases, this paper addresses its application to lattice models forstrongly interacting condensed phase systems, which constitute the other limiting case for fluids. The discrete modeling approachis based on the discrete energy classes of a lattice system of finite size, represented by a distribution of discrete localcompositions. In this way, the model uses the same level of discretization as classical statistical thermodynamics in terms of itspartition functions, yet avoids (1) a priori averaging of local compositions by utilizing a distribution, and (2) confinement tosystems of infinite size. The subsequent formulation of the probabilities of discrete energy classes serves as the basis forintroducing the concept of Shannon information, equivalent to thermodynamic entropy, and for deriving the equilibriumdistribution of probabilities by constrained maximation of entropy. The results of the discrete model are compared to thosederived from Monte Carlo simulations and by applying the Guggenheim model of chemical theory. We point out that thisapplicability of discrete modeling to systems of finite size suggests new possibilities for model development.

AB - Discrete modeling is a novel approach that uses the concept of Shannon entropy to develop thermodynamicmodels that can describe fluid-phase behavior. While previous papers have focused on reviewing its theoretical background andapplication to the ideal-gas model as one limiting case for fluid phases, this paper addresses its application to lattice models forstrongly interacting condensed phase systems, which constitute the other limiting case for fluids. The discrete modeling approachis based on the discrete energy classes of a lattice system of finite size, represented by a distribution of discrete localcompositions. In this way, the model uses the same level of discretization as classical statistical thermodynamics in terms of itspartition functions, yet avoids (1) a priori averaging of local compositions by utilizing a distribution, and (2) confinement tosystems of infinite size. The subsequent formulation of the probabilities of discrete energy classes serves as the basis forintroducing the concept of Shannon information, equivalent to thermodynamic entropy, and for deriving the equilibriumdistribution of probabilities by constrained maximation of entropy. The results of the discrete model are compared to thosederived from Monte Carlo simulations and by applying the Guggenheim model of chemical theory. We point out that thisapplicability of discrete modeling to systems of finite size suggests new possibilities for model development.

KW - Shannon entropy

KW - discrete modeling

KW - thermodynamic modeling

KW - maximum entropy principle

KW - lattice model

KW - local compositions

U2 - 10.1021/acs.iecr.5b04430

DO - 10.1021/acs.iecr.5b04430

M3 - Article

VL - 55

SP - 2483

EP - 2492

JO - Industrial & engineering chemistry research

JF - Industrial & engineering chemistry research

SN - 0888-5885

IS - 8

ER -