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 Eckart Schrank, Oliver Gaede, Michael G Trefry, Alison Ord, Bruce E Hobbs, Guy Metcalfe, Daniel Robert Lester

Research output: Chapter in Book/Report/Conference proceedingChapter (Report)Research


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.
Original languageEnglish
Title of host publicationBeyond the Second Law
Subtitle of host publicationEntropy Production and Non-Equilibrium Systems
EditorsRoderick C Dewar, Charles H Lineweaver, Robert K Niven, Klaus Regenauer-Lieb
Place of PublicationHeidelberg Germany
Number of pages13
ISBN (Electronic)9783642401541
ISBN (Print)9783642401534
Publication statusPublished - 2014
Externally publishedYes

Publication series

NameUnderstanding Complex Systems
ISSN (Print)1860-0832
ISSN (Electronic)1860-0840


  • 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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