Question

how to prove that gibbs state remains a gibbs state after evolution??​

Answer 1

ℏ✺ℓᾰ ժḙᾰԻ ℘ℓℨ ԻḙḟḙԻ т✺ ᾰ♭✺ṽḙ ᾰттᾰḉℏՊḙℵт ✌

Answer 2

Answer:

The density matrix is constant only when the evolution is Hamiltonian with the same Hamiltonian that is used in the definition. If some other Hamiltonian is used (for example, if some external perturbation is introduced), then the density matrix will evolve in non-trivial way.

So the "Gibbs state" will remain so only if the system is autonomouse, i.e. no external forces act on it.