The field of study is called Epigenetics [1]. I know practically nothing about it, but it seems that some of these alterations to the expression of DNA are not only persistent, but can also be inherited. Which is why some of these discoveries have been called a revenge of Lamarck over Darwin...

[1] https://en.wikipedia.org/wiki/Epigenetics

Epigenetic markers that appeared during the potato famine and Great Depression have been found in grandchildren of those who lived it.

There's also evidence healing from trauma can change expression.

What do you mean by persistent state?