It turns out that the Second Law of Thermodynamics is a special case of a more general result called Noether’s Theorem, which tells us that a differentiable symmetry of a system with conservative forces automatically generates/has it’s own conservation law, and the conservation of energy/the Second Law is a special case of this when the symmetry is time.
Here, a symmetry is a situation where a feature is preserved under transformations, and the fact that physics is time-symmetric, meaning that it doesn’t matter whether an identical physical process happens now, in the past, or in the future means that the Second Law of Thermodynamics/Conservation of Energy automatically pops out.
It is not a probabilistic statement, as long as we accept time-symmetry.
There is another derivation of the Second Law that is more specific to quantum mechanics, and this is also explanatory, but it’s pretty specific to our universe:
It turns out that the Second Law of Thermodynamics is a special case of a more general result called Noether’s Theorem, which tells us that a differentiable symmetry of a system with conservative forces automatically generates/has it’s own conservation law, and the conservation of energy/the Second Law is a special case of this when the symmetry is time.
Here, a symmetry is a situation where a feature is preserved under transformations, and the fact that physics is time-symmetric, meaning that it doesn’t matter whether an identical physical process happens now, in the past, or in the future means that the Second Law of Thermodynamics/Conservation of Energy automatically pops out.
It is not a probabilistic statement, as long as we accept time-symmetry.
https://en.wikipedia.org/wiki/Noether’s_theorem
There is another derivation of the Second Law that is more specific to quantum mechanics, and this is also explanatory, but it’s pretty specific to our universe:
https://www.quantamagazine.org/physicists-trace-the-rise-in-entropy-to-quantum-information-20220526/
Conservation of energy is not the same thing as the second law of thermodynamics.
Are you talking about the difference between the First and Second Laws of thermodynamics?
Yes.