Thanks, Michael, for a nice review of the various situations that, one way or another, naturally uphold the supremacy of the 2nd law of thermodynamics. Universality of this law as yet appears intact as far as the 'observed universe' is concerned. Probably, the biggest test of the law awaits its dictation when it comes to what will come out as phenomena interact to give rise to "megathonem?"

The second law is statistical in nature and the most rigorous definition is found in statistical mechanics. It is possible however to give a macroscopic interpretation. In macroscopic terms the second law is a mathematical statement for the empirical observation that the approach to equilibrium is a spontaneous process while the reverse process (removal from equilibrium) requires work. This again can be understood in terms of dissipation of gradients: Gradients produce a rate of transport in such a way that the gradient decreases. For example, heat flow from high to low temperature and as a result the temperature difference decreases (pressure gradients work exactly the same way). In equilibrium all macroscopic gradients cease: temperature and pressure are uniform. It is possible to generate a gradient inside an equilibrium system, but this requires work.

All of this is mathematically condensed in the inequality of the second law. When we say that the entropy of the universe never decreases we mean that with every process the universe overall gets closer to equilibrium, never further away. And while some part of the universe may move further away, other parts compensate by moving even closer to equilibrium.

Thanks, Themis, for your input. What intrigues me is the change of perception as one moves up or down the ladder of scale from the microscopic to the macroscopic realm or vice versa. Distinction between heat and work at the microscopic level becomes blurred (Thermal Physics -- C. Kittel & H. Kroemer). Now, between heat and work, what puts heat as degraded form of energy while work as superior form of energy, is entropy. Once distinction between and wok becomes blurred, what's the status of entropy?

Khalid, when it comes to entropy I prefer to think in terms of probabilities rather than mechanics: Entropy is S = -Σ pi log pi, where pi is the probability of outcome i. To say that a process is reversible is to say that we are certain about the number of outcomes; to say it is irreversible is to say that there are more outcomes than we initially thought. Where do these extra outcomes come from? From our incomplete knowledge of the process. A process is a change at the boundaries between system and surroundings. It is the incomplete knowledge of these interactions that give rise to irreversibility, except in the idealized case of reversible process, where we imagine this interaction to be the same as between two systems in equilibrium.

Does this make sense?

The deviation rate of the second law of thermodynamics is 14.6%. See the following figure (or annex). It's not a case.

* * * * * * * *

A: Figure 1 is from the authoritative book "Handbook for Estimating Gas-liquid Physical Properties", which calculates enthalpy change H1 by equation of state. From Fig. 1A, the accuracy of the equation of state is very high, but the enthalpy deviation rate derived is very large. The theoretical basis of the derivation is the thermal 2 differential equation.

B. Drawing with the deviation rate of state equation (< 1%) and enthalpy variation deviation rate (Fig. 2), without considering two abnormal points, the deviation rate is regularly arranged. The deviation rate of fitting line and Y axis intersection point C (0,0.146) and thermal 2 differential equation is 14.6%.

Logical error of the second law of thermodynamics:

1. There are many kinds of type 2 perpetual motion machines. Behind each type is a natural phenomenon.

Machine A: against the irreversibility of thermodynamics (diffusion, heat conduction, friction, etc) - dynamics;

Machine B: Utilizing the Difference of Carnot Efficiency (Reversible Thermodynamics) - Thermodynamics

2. A and B belong to different disciplines. There is a parallel relationship between them, and there is no logical mutual inevitability.

Heat 2 Logic: Experience induction, deny that A machine==》 B machine can not be manufactured==》 All material Kano efficiency: 1-T1/T2.

3. Logical of the second law of thermodynamics violates the physical logic that A and B cannot be inferred from each other.

4. the second law of thermodynamics elevates the "irreversibility", but it is only a kinetic experience.

5. See the annex for details.

The so-called "entropy " doesn't exist at all.

During the process of deriving the so-called entropy, in fact, ΔQ/T can not be turned into dQ/T. That is, the so-called "entropy " doesn't exist at all.

The so-called entropy was such a concept that was derived by mistake in history.

It is well known that calculus has a definition,

any theory should follow the same principle of calculus; thermodynamics, of course, is no exception, for there's no other calculus at all, this is common sense.

Based on the definition of calculus, we know:

to the definite integral ∫T f(T)dQ, only when Q=F(T), ∫T f(T)dQ=∫T f(T)dF(T) is meaningful.

As long as Q is not a single-valued function of T, namely, Q=F( T, X, …), then,

∫T f(T)dQ=∫T f(T)dF(T, X, …) is meaningless.

1) Now, on the one hand, we all know that Q is not a single-valued function of T, this alone is enough to determine that the definite integral ∫T f(T)dQ=∫T 1/TdQ is meaningless.

2) On the other hand, In fact, Q=f(P, V, T), then

∫T 1/TdQ = ∫T 1/Tdf(T, V, P)= ∫T dF(T, V, P) is certainly meaningless. ( in ∫T , T is subscript ).

We know that dQ/T is used for the definite integral ∫T 1/TdQ, while ∫T 1/TdQ is meaningless, so, ΔQ/T can not be turned into dQ/T at all.

that is, the so-called "entropy " doesn't exist at all.

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Why did the wrong "entropy" appear ?

In summary , this was due to the following two reasons:

1) Physically, people didn't know Q=f(P, V, T).

2) Mathematically, people didn't know AΔB couldn‘t become AdB directely .

If people knew any one of them, the mistake of entropy would not happen in history.

Please read my paper and those answers of the questions related to my paper in my Projects.

https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity