The problem

A cup of coffee or tea when left alone behaves in three evident ways: First, it cools if it is made hot, or heats up if it is iced. Second, it settles to a stationary state if stirred. Third, added cream spreads until uniformly mixed (accelerated by stirring). The reverse of these simple trends has never been observed.

In the mid-19th century, around the same time that the notion of energy was understood to be a conserved quantity in total, scientists also sought to explain why these trends appear to be universal, in systems like a cup of tea and every other observed system much larger and smaller. Such universality should be quantifiable like energy in a comprehensive physics theory. Logically, the entire universe must obey these trends as well, eventually settling to a state where nothing happens anywhere.

The conundrum is that these trends indicate continual “dissipation” of order with forward progress in time. This is contrary to the known laws of mechanics governing interaction between individual objects, which produce the same outcome whether time proceeds forward or backward. Scientists have pondered this apparent paradox for centuries without clear resolution.

Rudolph Clausius deduced a quantity in 1854 that distinguishes whether a process proceeds spontaneously in simple systems, and later named it “entropy” to combine a reference to energy with the Greek word for transformation. The theories of Classical Thermodynamics and Statistical Mechanics, by Josiah Gibbs in the 1870’s, developed plausible and surprisingly effective means to predict simple process outcomes, well before the modern era of atoms and quantum mechanics. They overcame the above paradox by axiom, the foremost being the Second Law of thermodynamics, stating that total entropy never decreases.

These axioms were deduced from the simplest examples of homogeneous, closed systems able only to exchange heat with and do mechanical work on the outside. Then they were postulated to be valid for all situations. This leap, though, hasn't yet been proven to be true. For practical process analysis, the difference between the simple case and more complex systems is bridged with empirical terms without theoretical basis.

These empirical terms are assumed to be a temporary measure until complete models of the specific participants is known. However, the new theory presented here implies that the Second Law itself is not valid for complex systems. Entropy may decrease! In which case, the concept of entropy loses its predictive power and standard theory lacks dynamic constraints necessary for a comprehensive theory of thermodynamics.

In contrast, the new theory presented here establishes a single, unambiguous logical structure for all applied physical analysis by understanding local mean flows, instead of assuming a static universal entropy condition. Equilibrium is simply the state where all flows are zero. The Second Law fails because zero flow generally depends on mode transition rates of the particles, which entropy neglects.