I’m wondering if people talk about this. Maybe you know?
Given a self-adjoint operator that’s bounded below and a density matrix on some Hilbert space, we can define for any a new density matrix
I would like to call this the thermalization of when is a Hamiltonian and where is the temperature and is Boltzmann’s constant.
For example, in the finite-dimensional case we can take to be the identity matrix, normalized to have trace 1. Then is the Gibbs state at temperature : that is, the state of thermal equilibrium at temperature
But I want to know if you’ve seen people do this thermalization trick starting from some other density matrix