Thermalization

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, th...