the violation of the second law of the thermodynamics can be shown by radiation heat transfer between two surface through curved mirror.It is explained on web page hsoylu.wordpress.com.

Using quantum entanglement:

https://www.quantamagazine.org/physicists-trace-the-rise-in-entropy-to-quantum-informat...

“'We like laws of physics to be exact,” said the physicist Chiara Marletto of the University of Oxford. Can the second law be tightened up into more than just a statement of likelihoods?

"A number of independent groups appear to have done just that. They may have woven the second law out of the fundamental principles of quantum mechanics — which, some suspect, have directionality and irreversibility built into them at the deepest level. According to this view, the second law comes about not because of classical probabilities but because of quantum effects such as entanglement. It arises from the ways in which quantum systems share information, and from cornerstone quantum principles that decree what is allowed to happen and what is not. In this telling, an increase in entropy is not just the most likely outcome of change. It is a logical consequence of the most fundamental resource that we know of — the quantum resource of information.

***

"Constructor theory aims to express all of physics in terms of statements about possible and impossible transformations. It echoes the way thermodynamics itself began, in that it considers change in the world as something produced by “machines” (constructors) that work in a cyclic fashion, following a pattern like that of the famous Carnot cycle, proposed in the 19th century to describe how engines perform work. The constructor is rather like a catalyst, facilitating a process and being returned to its original state at the end.

***

"The reason for the irreversibility, said Marletto, is that for most complex tasks, a constructor is geared to a given environment. It requires some specific information from the environment relevant to completing that task. But the reverse task will begin with a different environment, so the same constructor won’t necessarily work. “The machine is specific to the environment it is working on,” she said.

***

"Irreversibility is not just the most probable outcome but the inevitable one, governed by the quantum interactions of the components. “Our conjecture,” said Marletto, “is that thermodynamic irreversibility might stem from this.”

***

"The informational perspective on the second law is now being recast as a quantum problem. That’s partly because of the perception that quantum mechanics is a more fundamental description...But it also reflects the burgeoning interest in quantum information theory itself. We can do things with information using quantum principles that we can’t do classically. In particular, entanglement of particles enables information about them to be spread around and manipulated in nonclassical ways. (my bold)

"Crucially, the quantum informational approach suggests a way of getting rid of the troublesome statistical picture that bedevils the classical view of thermodynamics, where you have to take averages over ensembles of many different microstates. “The true novelty with quantum information came with the understanding that one can replace ensembles with entanglement with the environment,” said Carlo Maria Scandolo of the University of Calgary.

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"The resource-theory approach, said physicist Markus Müller of the University of Vienna, “admits a fully mathematically rigorous derivation, without any conceptual or mathematical loose ends, of the thermodynamic laws and more.” He said that this approach involves “a reconsideration of what one really means by thermodynamics” — it is not so much about the average properties of large ensembles of moving particles, but about a game that an agent plays against nature to conduct a task efficiently with the available resources."
(my bold)

Comment: refining the second law involves quantum mechanics and information, the two bases of our reality. Note my bolds. God's work in design is not easy to unravel.