Until I read this thread I would have agreed with that, but Helio earlier on has provided a good reason as to why the first law of thermodynamics may not apply in some circumstances, have you read that. In that particular discussion I was trying to use the first law of thermodynamics to prove that existence is eternal, but Helio threw a spanner in the Works. I do have a workaround for this and I'll post it later, so for now I will still say existence is eternal but that's another topic for later.
IG said - "By that logic, Cat, our thoughts and our ideas live on forever, but they won't remain the same."
I think you would need absolute determinism for that idea to work, because as you are suggesting if quantum mechanics introduces some randomness at a fundamental level then your thoughts and ideas will get scrambled up too much. If determinism is correct your thoughts and ideas will leave trails of cause and effect behind them Forever After.
IG said - "Our thoughts and ideas are stored by complex molecules of organic chemistry in our brain (I don't know much about organic chemistry, but I guess, you might know). But, the thing is, they are ever-changing."
Yes, but as earlier, I split that into 2, I suggested that thoughts are arrangements of moving atoms and molecules and that memories were fixed arrangement of atoms and molecules, but sure, memories are changing as well.
IG said - "thousands of reactions are happening in my brain and my whole body that is changing the structures of everything that exists in our body! That is indeed a subject to ponder on! A wonderful subject indeed."
Yes wonderful indeed, why not include my statement from earlier where I said that the atoms in the president's brain instruct the motor department in his brain to pick the phone up and tell his general to go to War. So not only do the reactions in your brain change the structures in your body, they also have the power to change the structure of the whole world!