That’s a far cry from the evolution of sentient beings from primordial mud and would certainly not violate the laws of science.
Leaving entropy out of it, in recorded history how many species have gone extinct and how many distinct species have come
Into being? Evolution is not happening because it can’t. Mutation, adaptive traits sure, new distinct species, not so much.
That's a loaded question, because
a. Distinct 'Species' are a human construct not a scientific definition (mostly).
b. All species are a spectrum.
For example.
You take a plant from Europe, dump it in America.
It now lives in a different ecological niche. It's pollinated by different insects. It sees different weather. It's competing with different plants. Its roots capture nitrogen through entirely different symbiotic relationships with different organisms. Over time, genetic drift happens to the population and it begins to exhibit different physical characteristics.
At what point do
we decide it's an entirely new species?
The usual distinction is when it can no longer interbreed and create viable offspring.
If we do adopt that definition, it's definitely happened numerous times in recorded history.
One that is relevant to my industry: S. cerevisiae and S. pastorianus. Lager yeast and ale yeast. Not able to interbreed, genetically distinct, genetic drift studies put the split around the year 1300, which is consistent with the first recorded production of bottom fermenting lager beers.
The culprit; hybridization leading to a genetically distinct hybrid that was a. unable to breed with the species of either parent, b. self sustaining. A lot easier to do that with a species that reproduces asexually of course.
This happens all the time. It's not uncommon. It's actually more common now than would be 'normal', because humans are really good at inadvertently putting species in ecological niches they weren't adapted to, and applying novel selective pressures. Rats in Australia, Tomatoes in Europe, speciation in bacteria due to human selective mechanisms such as antibiotics, etc, etc.
Here's a link to a reference dump of a load of examples:
So to answer your original question: Lots of species have gone extinct. Lots of new species have evolved. Both have happened many times in recorded history. We
think more have gone extinct than have evolved leading to a reduction in genetic diversity, but considering we've only characterized a tiny fraction of all species that exist anyway... who really knows.