My approach
Current theory in any discipline represents the body of knowledge accumulated from past experience. Naturally, this body must be considered a solid foundation in order to make new discoveries. I tend to view theory as made of individual "bricks" of relatively firm, tried-and-true methods and observations bound together by soft intuition and conventional wisdom. Theories then are created and modified in a continual process with whatever bricks and ideas are available at the time.
The "mortar" of conventional wisdom often hardens into a solid structure with minor settling of the embedded bricks. Some regions remain soft, though, because they do not mesh with the evolving theory, indicating that the solid facts need to be rearranged with different rationale. This rearrangement might be slight, causing little disturbance to the theory built atop, or occasionally might be revolutionary, allowing people to perform in undreamed of ways. Such advances come only from exhaustively prodding theory for soft spots and then testing alternative methods and rationale.
The standard theory of thermodynamics has been very successful in connecting a vast array of solid observations. But in 170 years, the "mortar" of entropy has not set. It remains as opaque and vague as when it was proposed. The Second Law of thermodynamics, stating that entropy never decreases universally, is the founding concept of the standard theory and so it has been hard to see how it could be wrong without toppling the entire structure. Most scientists believe it is a fundamental physical law. Who would undertake such a quixotic quest to replace the Second Law?
I have always been skeptical of entropy in my schooling and teaching college and graduate physics courses. I could parrot the standard thermodynamics arguments but didn't feel competent to explore off the beaten path. The theory seems mostly to "predict after the fact." Various interpretations of entropy have been found to justify known results but there seems to be little consensus on new situations. It appears to me that an acceptable explanation for any new result involves a series of publications to justify the chosen interpretation of entropy. This strikes me as odd for an established theory. The physics of collisions is well understood. Why should the effect of many individual collisions be so mysterious?
I began with the question, "how would I explain the physics of many body systems to someone who knows only basic mechanics and has never heard of entropy?" The explanation must build logically step by step on this foundation. A quantum basis is necessary to describe microscopic activity generally. Yet, surprisingly, no comprehensive attempt has been presented to date. Effort has focused instead on proving the Second Law.
The task required dismantling the entire wall of science, chipping away all vestiges of entropy, and then creating a rationale that connects seamlessly with physics on the ground below and fits all bricks into the same structure up top as the current applied theories. My approach bore fruit particularly in producing general transport equations describing the essential activity of particle transformations. This result is an evident advance over standard theory, which is limited to assumed empirical laws for transport. All dynamics are treated in a unified manner: phase transitions, chemical transformations, particle and heat diffusion, material stress and friction. Furthermore, all empirical "bricks" and subsidiary applied science theories remain intact despite rebuilding their foundation!
Using a mountaineering analogy, the pioneers of thermodynamics approached the theoretical summit from the only direction available at the time, given their limited understanding of atoms and energy. They invented technical methods to overcome seemingly unassailable pitches and amazingly found a route to near the peak. Our understanding of the microscopic world has expanded enormously since then. In pursuing a clearer explanation from modern physics, I found that the back side of the mountain is a gradual slope in comparison to the craggy face that the pioneers tackled. The apparatus of entropy is not required after all. And without this apparatus, it is easier to explore the complicated terrain of thermodynamics encompassing all fields of applied physical science, particularly the interdisciplinary regions that will likely be a focus of future research.
More surprising, even as my theory diverged from standard theory, I did not expect to reveal a clear contradiction implying that the Second Law is generally invalid, as well as unnecessary. Such a disruptive claim must be supported with detailed argument that I have given in Thermodynamics Without Entropy. The ease with relatively simple logic and unambiguous interpretation that a variety of applications are demonstrated in this treatise hopefully inspires confidence in the new theory.