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Degradation-Entropy Generation Methodology

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The Degradation-Entropy Generation (DEG) Methodology is based on the Degradation-Entropy Generation (DEG) theorem,[1] which directly correlates a system’s degradation/transform measure with the irreversible entropies generated by the active dissipative processes that underlie the degradation. The DEG theorem was proposed by Michael D. Bryant, Michael M. Khonsari and Frederick F. Ling. The new DEG methodology, which combines existing degradation measures with instantaneous—often unsteady—entropy generation, was developed by Jude A. Osara [2] and Michael Bryant at The University of Texas at Austin.


The concept of relating degradation to entropy grew from a 1997 Workshop on Maintenance Science at The University of Texas at Austin, organized by Frederick Ling of UT-Austin, Marty Wortman and Georgia Klutke of Texas A&M College Station. Here the prime recommendation of representatives from industry, government and university was to develop better models to predict equipment degradation. This led Ling and Wortman to the Thermodynamic Degradation paradigm, that hypothesized that degradation could be related to entropy. Via data measured from copper rubbing steel, [3][4] Frederick Ling, Michael Bryant and their students correlated degradation in the form of surface wear to the entropy produced by friction during rubbing, and mathematically related wear to entropy. Later rubbing measurements by Michael M. Khonsari with different materials again supported the Thermodynamic Degradation paradigm. This led Bryant, Khonsari and Ling to propose and prove the Degradation-Entropy Generation theorem in a Royal Society of London Proceedings article.[1] Multiple articles applying the DEG theorem [5][6][7][8] followed these seminal works.

Based on the thermodynamic State Postulate and free energies—the Helmholtz and Gibbs potentials—Jude Osara, in his doctoral thesis [2] at UT-Austin's Mechanical Engineering department and subsequent research articles [9][10][11][12] co-authored with his doctoral adviser Michael Bryant, derived new formulations for entropy generation which extended the DEG theorem to unsteady, spontaneous and nonlinear degradation, and led to the discovery of the existence of a system-characteristic multi-dimensional orthogonal degradation-entropy generation space. In these works, measured data from dissipative loading of lithium-ion and lead-acid batteries, lubricating grease and steel rod were used to demonstrate the DEG methodology.


  1. 1.0 1.1 Bryant, M.d; Khonsari, M.m; Ling, F.f (2008-08-08). "On the thermodynamics of degradation". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 464 (2096): 2001–2014. doi:10.1098/rspa.2007.0371.
  2. 2.0 2.1 Osara, Jude Asuelimen, author. The thermodynamics of degradation. OCLC 993882550.CS1 maint: Multiple names: authors list (link) Search this book on
  3. Doelling, K. L.; Ling, F. F.; Bryant, M. D.; Heilman, B. P. (September 2000). "An experimental study of the correlation between wear and entropy flow in machinery components". Journal of Applied Physics. 88 (5): 2999–3003. doi:10.1063/1.1287778. ISSN 0021-8979.
  4. Ling, F.F; Bryant, M.D; Doelling, K.L (December 2002). "On irreversible thermodynamics for wear prediction". Wear. 253 (11–12): 1165–1172. doi:10.1016/s0043-1648(02)00241-7. ISSN 0043-1648.
  5. Bryant, Michael D.; Khonsari, Michael M. (2008-01-01). "Application of Degradation-Entropy Generation Theorem to Dry Sliding Friction and Wear". STLE/ASME 2008 International Joint Tribology Conference. ASMEDC: 1–3. doi:10.1115/ijtc2008-71079. ISBN 978-0-7918-4336-9.
  6. Bryant, Michael (2009). "Entropy and Dissipative Processes of Friction and Wear". Wear.
  7. Bryant, Michael (2010). "Unification of friction and wear. In Recent Developments in Wear Prevention, Friction and Lubrication". Research Signpost.
  8. Bryant, Michael D. (2016-10-01). "On Constitutive Relations for Friction From Thermodynamics and Dynamics". Journal of Tribology. 138 (4). doi:10.1115/1.4032821. ISSN 0742-4787.
  9. Osara, Jude; Bryant, Michael (2019-04-03). "A Thermodynamic Model for Lithium-Ion Battery Degradation: Application of the Degradation-Entropy Generation Theorem". Inventions. 4 (2): 23. doi:10.3390/inventions4020023. ISSN 2411-5134.
  10. Osara, Jude A.; Bryant, Michael D. (2019). "Thermodynamics of Lead-Acid Battery Degradation: Application of the Degradation-Entropy Generation Methodology". Journal of the Electrochemical Society. 166 (16): A4188–A4210. doi:10.1149/2.0651916jes. ISSN 0013-4651.
  11. Osara, Jude A.; Bryant, Michael D. (September 2019). "Thermodynamics of grease degradation". Tribology International. 137: 433–445. doi:10.1016/j.triboint.2019.05.020. ISSN 0301-679X.
  12. Osara; Bryant (2019-07-12). "Thermodynamics of Fatigue: Degradation-Entropy Generation Methodology for System and Process Characterization and Failure Analysis". Entropy. 21 (7): 685. doi:10.3390/e21070685. ISSN 1099-4300.

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