On February 5, 2021, Casper A. Helder posted the question “can the second law of thermodynamics be abandoned?” I was surprised to read that the second law )together with the first law( the only two laws that remain unchanged since their formulation by Clausius in 1867, are boldly doubted. Moreover, the entropy in which its propensity to grow is the second law is not even mentioned, and therefore, I wrote a short cynical answer. To my surprise every few days since I followed this question, more people add answers and for today, there are 6618 reads and 386 answers! For Example, Henning Struchtrup a professor at Victoria university working in the field wrote: “No doubt one can criticize Carnot or Clausius but one should not forget that they were at the very beginning”. Struchtrup received 13 recommendations for his answers. I wonder what causes a respectful scientist from this field to say that no doubt that Carnot and Clausius's works are problematics.
From reading part of the answers including Helder's argumentation, I believe that somehow in the last century, the definition and therefore the meaning of the second law was forgotten. Hereafter, I will summarize the definition of the second law and its immediate consequences.
2nd Law Definition: In any irreversible process, the entropy S increases.
Irreversibility: If we have a reservoir at a temperature T and one adds an amount of energy Q in an irreversible route its entropy increases by S>Q/T. If the process is reversible then the entropy increase is S=Q/T. This inequality is called Clausius inequality.
The amount of energy added or removed from a reservoir is a measurable quantity. However, we see that in an irreversible path "T" is smaller than T in a reversible path of the same system. Therefore, we cannot define temperature and therefore entropy for a system, in an irreversible route.
Equilibrium: If a closed system is resting for a long time its entropy will increase to the maximum. Clausius inequality means that energy flows from hot to cold and therefore in equilibrium all the subsystems of an ensemble have equal temperature i.e. all its degrees of freedom have the same amount of energy i.e. in an ideal gas every degree of freedom of any molecule has kT/2 energy. Here k is the Boltzmann constant, which is the gas constant, divided by the Avogadro number and T is the temperature. Moreover, in equilibrium, all the microstates (a distinguishable configuration of any ensemble) have an identical amount of energy. Therefore,
Temperature and Entropy are defined only for systems in Equilibrium: to find the temperature of an ensemble in equilibrium one can take a single molecule measure its energy and know the temperature. However, this is seldom the case. Usually, there are “hotter” molecules and “colder” ones and this is the reason why both the entropy and temperature are defined only in equilibrium. This ambiguity about the “temperatures” out of equilibrium causes all kinds of anomalous behaviors like “super cooling” and the Mpemba paradox. This is why the application of the 2nd law has difficulties in microscopic systems. These phenomena are proving Clausius's inequality and the second law rather than disproving it.
Maximum Entropy and Quantum theory. Since in equilibrium the entropy expression of a system is maximum, every ensemble tends to reach spontaneously equilibrium. Therefore, one can calculate many properties of an ensemble by maximizing the statistical expression of the entropy (Max Entropy Technique). Planck did such a calculation for EM radiation in equilibrium with a materialistic body and found the quantized nature of energy. Is abandoning the 2ndlaw means giving up the Quantum theory? Can physics without entropy exist?
I post this question to find out if there is any concrete scientific evidence or argumentation that may cause scientists to declare that there is serious criticism against Clausius's inequality, Carnot's efficiency, and the second law.