I really think you should study more; your questions border on insanity.
Well, permit me to try again. You referred to "the absolute truth of conflict between the laws of thermodynamics and evolution". So if the laws of thermodynamics conflict with evolution, even presumptively, let alone absolutely, then why doesn't life itself?
Surely the thermodynamic cost of, say, changing a DNA base pair cannot be greater than the thermodynamic cost of, say, creating a molecule of ATP (the cell's energy source). Yet a typical animal must create, what, millions?, billions?, trillions?, of ATP molecules every single hour. I don't know what the numbers are exactly, but surely in the space of hours a human has created more molecules of ATP than the number of DNA base pair differences that separate humans and chimpanzees.
Life overcomes entropy -- concentrates negative entropy -- in the first instance, prior to and apart from evolution. So how does evolution contradict thermodynamics without life itself doing so first?