Shortly after the decision to pursue a PhD degree, I had to choose a PhD research subject. My search for a relevant, yet interesting topic led to a meeting with Prof. Bryant and the start of my involvement in the DEG development. At the end of the first DEG discussion, I was almost certain this would be my PhD research subject, albeit only understanding about 20% of content discussed. The choice turned out much easier than anticipated due to a few key factors:

• Prof. Bryant seemed 100% certain. “The DEG works”, he would say emphatically with a forward nod that added, “I guarantee it.” His enthusiasm was palpable and infectious.

• Thermodynamics, I always found fascinating. This indeed would be enjoyable work, I envisaged.

• Did someone say degradation of everything? Does that mean I get to work on a number of completely different systems? Even less boring!

Before me was a relevant and interesting doctoral research subject: thermodynamic modeling of real system degradation – formulate and experimentally verify DEG models for two or more systems. The decision was made.

Soon afterwards, another realization hit: I had neither an inkling what the final product would look like nor an idea how I was going to get it done. Fortunately, Profs. Michael Bryant, Michael Khonsari and Frederick Ling had already done significant work in establishing the DEG theorem [1][2], having previously applied the proposed structured approach to friction and wear [2], details in chapter 1; so, there was sufficient material to study. Grease (the lubricant, not the movie) was selected first for experimental demonstration, with others to come later.

... during which I learned more real-world engineering and partly developed what would become invaluable practical results-oriented, problem-solving intuition. While I was away on full-time employment, hence the hiatus and consequent increase in static inertia (for the Engineering Mechanics enthusiast), Prof. Bryant continued to publish works on system degradation including a chapter in Jonathan Singler's The Physics of Degradation in Engineered Materials and Devices. Without new experiments, he would derive governing thermodynamic relations for various systems and obtain DEG coefficients via direct analogy with previously established system-process characterization models, an approach later inherited in my dissertation study.

It was 1pm at Posse East (informal venue of several hundreds of routine science/engineering team lunch meetings annually, including ours). “Jude, we know we can do the work. But just knowing is not enough. We actually have to get it done. Let’s get it done”, Prof. Bryant concluded, as we rose for the stroll back to the department building. While I was away, his interest in batteries had heightened, and with the obvious significance of portable energy, we selected batteries – lithium-ion and lead-acid – for second DEG application. Due to my interest in fatigue analysis and recent work experience, we decided fatigue was next in line, but the potential challenges in characterizing grease and batteries left DEG’s fatigue application yet a distant thought at the time.

Over the next 2.5 years, I would study over 200 book sections and technical papers, perform several grease and battery experiments, process hundreds of severely nonlinear data, consume several Posse East burgers and fries - with carbonated soft drinks for the 'wash down', write a doctoral thesis [1], establish EnHeGi and present DEG to a few potential industry users. Nevertheless, the highlight of this period remains the emergence of a universal real-time system degradation methodology, with variegated experimental verifications.

Now for some scientific narrative.

In addition to presenting a background for new developments, all independent research studies start with a review of past and current works in the specific field. Thermodynamics is a well-established broad field of science that has long been and continues to be used in design and analysis of several engineering systems and processes, from power generation to transportation. This section briefly reviews relevant foundational thermodynamic principles, from equilibrium to non-equilibrium Thermodynamics as they relate to real-world systems and processes.

Classical Thermodynamics [3-5]

Applying energy conservation to the heat engine, the first law of thermodynamics states that the change in internal energy of a system is the difference between the heat supplied to it and the consequent work obtained from it. In mathematical notation,

 ∆U = Q – W .       (1)

The first law gives the best-case scenario for ALL things, notwithstanding the apparent obscurity of that esoteric deduction from equation (1). (Unfortunately, its demystification will make for an overly long article, hence the interested reader should consult a good thermodynamics textbook - see REFERENCES below). To account for waste heat that never gets converted into work but disorganizes the system, the second law of Thermodynamics introduces entropy as a measure of this disorganization which, if not reversed, results in permanent degradation of the system. Stated mathematically as the Clausius inequality (named after Rudolf Clausius, who first came up with the expression),

 ∆S ≥ (Q / T)b ,       (2)

a system’s entropy change as it undergoes a process is greater than or equal to the entropy transfer across its boundaries b. This inequality has since been simplified into the more useful

 ∆S = (Q / T)b + S'        (3)

which is specific and easier to evaluate and interpret: the total entropy change taking place in a closed system as it undergoes a process is the sum of entropy transfer across the system's boundaries and entropy generation within its boundaries. The second law prescribes the real-world scenario. In these two fundamental laws, the capabilities of thermodynamics are deeply rooted. Formulations such as equations (1) and (3) form the basis of several important engineering systems such as combustion – including jet propulsion – engines, steam power plants and air-conditioning/refrigeration systems. However, many everyday systems do not operate on energy conversion between heat and mechanical work, and this may have limited the application of thermodynamics in other areas of engineering, e.g. characterization of electrical/electronic systems.

A first-law analysis tells us the best a system can do so we can decide early if the venture is worth initiating. A second-law analysis tells us the actual expected output from a given combination of input system parameters. Therefore, it is not far-fetched that a combined first and second law analysis would consistently anticipate, and can be used to tune or optimize a system’s performance, both in the design stage and during operation.

A major feature of classical thermodynamics is the frequent use of mathematical manipulations, which may have attracted quite a few theoretical mathematicians and physicists. Thermodynamic models, taking advantage of phenomenological evolution common to all real systems (with very high accuracy when experiments are controlled), are typically of the first order. In all of theoretical thermodynamics, Prof. Herbert Callen's thermodynamic postulates [7] are peradventure the farthest-reaching and most experimentally verified. I find it interesting that he would conduct a simple experiment every now and then, perhaps to prove his formulations to experimental thermodynamicists. The next 3 sub-sections adapt Callen's definitions to everyday systems.

Of States and Paths – Equilibrium and Non-Equilibrium

(coming soon)

Energy Minimum and Entropy Maximum

(coming soon)

Free Energies or Thermodynamic Potentials

"... a battery with an 80% drop in internal energy is more useful (has more electrochemical potential or free energy) in supplying electric charge through direct interaction than a freshly cut diamond, so an internal energy analysis conducted for both components is subject to misinterpretation." – Jude Osara (Thermodynamics of Degradation, 2017)

(coming soon)

Non-Equilibrium Thermodynamics [6-8]

Often given credit for the advent of modern thermodynamics, Theophile de Donder introduced the first entropy balance for chemical reactions (a more specific version of equation (3)), simplifying the Clausius inequality (equation (2)) and setting the foundation for analytical Irreversible Thermodynamics. Another significant contribution of his work is the chemical affinity which has since established thermodynamic analysis of chemical reactions, and is directly related to a battery's voltage. Prof. de Donder’s former PhD student and future Nobel laureate Ilya Prigogine extended these formulations to non-reacting systems (equation (3)), further establishing and broadening the applicable scope of Irreversible Thermodynamics. Prof. Prigogine focused his research on far from equilibrium interactions which Classical Thermodynamics appeared hitherto unable to characterize. His expansive study of fluctuating and unstable systems led to his discovery of dissipative structures, special systems formed from internal self-reorganizing response to severe energy dissipation. (Our experimental battery measurements recently revealed inadvertent emergence of a dissipative structure; more on this in a future technical paper).

Extending equilibrium thermodynamics to non-equilibrium thermodynamics of macroscopic systems, Prof. Prigogine showed via his minimum entropy production theorem that irreversible entropy produced by a steady state process YdX is simply JdX where J=Y/T is thermodynamic force and dX is thermodynamic flow. This equation is often found in textbooks and research works that apply Thermodynamics to real system modeling. However, Prigogine also listed three basic assumptions for the validity of this expression:

1. Linear phenomenological laws;

2. Validity of Onsager’s reciprocity relations;

3. Phenomenological coefficients may be treated as constants.

Of particular note are the first and third assumptions requiring that the physical law governing the process be linear and that process coefficients be constant, conditions that readily favor Onsager’s reciprocity, the second assumption. In applying existing scientific laws to real-world applications especially nonlinear processes, it is well known that these assumptions limit validity of principles such as the minimum entropy production theorem to linear transformations and can reduce the accuracy of real system analysis results.

Fluctuations and Instability

  "Chaos gives rise to order." – Ilya Prigogine (Time, Structure and Fluctuations – Nobel Lecture, Dec. 8, 1977)

 (coming soon)

While science primarily deals with investigating, establishing and verifying natural laws/theories, engineering takes the next step of applying scientific discoveries to everyday applications. Here, I briefly review common thermodynamic systems, such as internal combustion engines and refrigerators, as well as a few recent and ongoing real-world applications of thermodynamics – for system/process characterization and analysis.  Note that the applications listed below are those I have studied and are by no means exhaustive of existing thermodynamic characterizations.

The Heat Engine – ICEs, Turbines, Compressors, Heat Exchangers [12–14]

(coming soon)

Prof. Adrian Bejan's Entropy Generation Minimization [15–17]

(coming soon)

Prof. Cemal Basaran's Unified Mechanics Theory [18–22]

(coming soon)

Prof. Erik Kuhn's Grease Rheological Energy Density [23–28]

(coming soon)

Prof. Michael Khonsari et al's Fatigue Entropy [29–38]

(coming soon)

Profs. Leonid A. Sosnovskiy and Sergei S. Sherbakov's Mechanothermodynamics [39–41]

(coming soon)

Profs. Michael Bryant and Frederick Ling's Friction and Wear Entropy [2–6]

(coming soon)

[1] Osara J. A. The Thermodynamics of Degradation. Doctoral Thesis, UT Austin; 2017.

[2] Doelling K. L., Ling F. F., Bryant M. D. and Heilman B. P. An Experimental Study of the Correlation Between Wear and Entropy Flow in Machinery Components. Journal of Applied Physics; 2000.

[3] Bryant M. D., Khonsari M. M., Ling F. F. On the Thermodynamics of Degradation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences; 2008.

[4] Ling F. F., Bryant, M. D., Doelling K. L. On Irreversible Thermodynamics for Wear Prediction. Wear; 2002.

[5] Bryant M. D. Entropy and Dissipative Processes of Friction and Wear. FME Transactions; 2009.

[6] Bryant M. D. On Constitutive Relations for Friction from Thermodynamics and Dynamics. Journal of Tribology; 2016.

[7] Burghardt M. D., Harbach J. A. Engineering Thermodynamics. 4th ed. HarperCollins College Publishers; 1993.

[8] DeHoff R. T. Thermodynamics in Material Science. 2nd ed. CRC Press; 2006.

[9] Callen H. B. Thermodynamics and an Introduction to Thermostatistics. John Wiley & Sons, Ltd; 1985.

[10] Prigogine I. Introduction to Thermodynamics of Irreversible Processes. Charles C Thomas; 1955.

[11] de Groot S. R. Thermodynamics of Irreversible Processes. North-Holland Publishing Company; 1951.

[12] Kondepudi D., Prigogine I. Modern Thermodynamics: From Heat Engines to Dissipative Structures. John Wiley & Sons Ltd; 1998.

[13] Moran, M. J., Shapiro, H. N. Fundamentals of Engineering Thermodynamics, 5th ed. Wiley, 2004.

[14] Cengel Y. A., Boles M. A. Thermodynamics: An Engineering Approach, 8th ed. McGraw Hill; 2015.

[15] Bejan A. The Method of Entropy Generation Minimization. Energy and the Environment; 1990.

[16] Bejan, A. Advanced Engineering Thermodynamics. 3rd ed. John Wiley & Sons, Inc; 1997.

[17] Bejan A. Method of entropy generation minimization, or modeling and optimization based on combined heat transfer and thermodynamics. Revue Générale de Thermique; 1996.

[18] Gomez, J.; Basaran, C. A thermodynamics based damage mechanics constitutive model for low cycle fatigue analysis of microelectronics solder joints incorporating size effects. Int. J. Solids Struct. 2005.

[19] Gomez, J.; Basaran, C. Damage mechanics constitutive model for Pb/Sn solder joints incorporating nonlinear kinematic hardening and rate dependent effects using a return mapping integration algorithm. Mech. Mater. 2006.

[20] Basaran, C.; Lin, M.; Ye, H.Athermodynamic model for electrical current induced damage. Int. J. Solids Struct. 2003.

[21] Basaran, C.; Nie, S. An Irreversible Thermodynamics Theory for Damage Mechanics of Solids. Int. J. Damage Mech. 2004.

[22] Basaran, C.; Gomez, J.; Gunel, E.; Li, S. Thermodynamic Theory for Damage Evolution in Solids. In Handbook of Damage Mechanics; Voyiadjis, G., Ed.; Springer: New York, NY, USA, 2014.

[23] Kuhn E. An energy interpretation of thixotropic effects. Wear; 1991.

[24] Kuhn E. Description of the Energy Level of Tribologically Stressed Greases. Wear; 1995.

[25] Kuhn E. and Balan C. Experimental Procedure for the Evaluation of the Friction Energy of Lubricating Greases. Wear; 1997.

[26] Kuhn E, Investigations into the Degradation of the Structure of Lubricating Greases. Tribology Transactions; 1998.

[27] Kuhn E. Correlation between System Entropy and Structural Changes in Lubricating Grease. Lubricants; 2015.

[28] Kuhn E. Friction and Wear of a Grease Lubricated Contact — An Energetic Approach in Tribology - Fundamentals and Advancements, J. Gegner, Ed. Intech; 2013.

[29] Amiri M. and Khonsari M. M. Life Prediction of Metals Undergoing Fatigue Load Based on Temperature Evolution. Materials Science and Engineering A; 2010.

[30] Naderi M. and Khonsari M. M. An Experimental Approach to Low-Cycle Fatigue Damage Based on Thermodynamic Entropy. International Journal of Solids and Structures; 2010.

[31] Naderi M. and Khonsari M. M. A Thermodynamic Approach to Fatigue Damage Accumulation Under Variable Loading. Materials Science and Engineering A; 2010.

[32] Naderi M. and Khonsari M. M. Real-Time Fatigue Life Monitoring Based on Thermodynamic Entropy. Structural Health Monitoring; 2011.

[33] Amiri M., Naderi M. and Khonsari M. M. An Experimental Approach to Evaluate the Critical Damage. International Journal of Damage Mechanics; 2011.

[34] Naderi and Khonsari M. M. A Comprehensive Fatigue Failure Criterion Based on Thermodynamic Approach. Journal of Composite Materials, vol. 46, no. 4; 2012.

[35] Naderi M. and Khonsari M. M. Thermodynamic Analysis of Fatigue Failure in A Composite Laminate. Mechanics of Materials; 2012.

[36] Naderi M. and Khonsari M. M. On the Role of Damage Energy in the Fatigue Degradation Characterization Of A Composite Laminate. Composites Part B: Engineering; 2013.

[37] Amiri M. and Modarres M. An Entropy-Based Damage Characterization. Entropy; 2014.

[38] Naderi M., Amiri M. and Khonsari M. M. On the Thermodynamic Entropy of Fatigue Fracture, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences; 2010.

[39] Sosnovskiy L. A. and Sherbakov S. S. Surprises of TriboFatigue; 2009.

[40] Sosnovskiy L. A. and Sherbakov, S. S. Mechanothermodynamical System and Its Behavior. Contin. Mech. Thermodyn; 2012.

[41] Sosnovskiy L. A. and Sherbakov S.S. Mechanothermodynamic Entropy and Analysis of Damage State of Complex Systems. Entropy; 2016.

[42] Osara J. A. and Bryant M. D. Thermodynamics of Grease Degradation. Tribology International, 2019.

[43] Osara J. A. and Bryant M. D. A Thermodynamic Model for Lithium-Ion Battery Degradation: Application of the Degradation-Entropy Generation Theorem. Inventions, 2019.

[44] Osara J. A. and Bryant, M. D. Thermodynamics of Fatigue: Degradation-Entropy Generation Methodology for System and Process Characterization and Failure Analysis. Entropy, 2019.

[45] Osara J. A. Thermodynamics of Manufacturing Processes: The Workpiece and the Machinery Inventions, 2019.

[46] Osara J. A. and Bryant M. D. Thermodynamics of Lead-Acid Battery Degradation: Application of the Degradation-Entropy Generation Methodology. Journal of the Electrochemical Society, 2019.