Beyond the Second Law pp 323-335

Part of the Understanding Complex Systems book series (UCS) | Cite as

Entropic Bounds for Multi-Scale and Multi-Physics Coupling in Earth Sciences

  • Klaus Regenauer-Lieb
  • Ali Karrech
  • Hui Tong Chua
  • Thomas Poulet
  • Manolis Veveakis
  • Florian Wellmann
  • Jie Liu
  • Christoph Schrank
  • Oliver Gaede
  • Mike G. Trefry
  • Alison Ord
  • Bruce Hobbs
  • Guy Metcalfe
  • Daniel Lester
Chapter

Abstract

The ability to understand and predict how thermal, hydrological, mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal–Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties, stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.

Keywords

Thermodynamics Multi-scaling THMC coupling Numerical simulations Dissipative structures Finite time thermodynamics Maximum entropy production  Minimum entropy production Thermodynamic homogenization methods 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Klaus Regenauer-Lieb
    • 1
    • 2
  • Ali Karrech
    • 7
  • Hui Tong Chua
    • 3
  • Thomas Poulet
    • 2
  • Manolis Veveakis
    • 2
  • Florian Wellmann
    • 2
  • Jie Liu
    • 1
  • Christoph Schrank
    • 4
  • Oliver Gaede
    • 4
  • Mike G. Trefry
    • 1
    • 6
  • Alison Ord
    • 1
  • Bruce Hobbs
    • 1
  • Guy Metcalfe
    • 5
  • Daniel Lester
    • 5
  1. 1.School of Earth and EnvironmentThe University of Western AustraliaCrawleyAustralia
  2. 2.CSIRO Earth Science and Resource EngineeringBentleyAustralia
  3. 3.School of Mechanical and Chemical EngineeringThe University of Western AustraliaCrawleyAustralia
  4. 4.Earth, Environmental and Biological Sciences SchoolQueensland University of TechnologyBrisbaneAustralia
  5. 5.CSIRO Mathematics, Informatics and StatisticsApplied Fluid Chaos GroupHighettAustralia
  6. 6.CSIRO Land and WaterFloreat ParkAustralia
  7. 7.School of Earth and EnvironmentThe University of Western AustraliaCrawleyAustralia

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