>>13065162 Interpreting as the inverse temperature, the thermal state is just a mixture of eigenstates of weighted by their Boltzmann factors.
Not sure what you mean by
>what does it measure physically?but keep in mind that a Wick rotation isn't a physical transformation. It's just a convenient mathematical tool. In this case, it lets us relate pure-state dynamics with static mixed-state properties, . I suppose the real physical connection would be if you embed the Hilbert space , on which acts, into a larger environment, . The Lindblad master equation for this system no longer necessarily describes unitary evolution anymore. Let be the Lindbladian, describing both the system dynamics , environment dynamics, and interaction terms between system and environment. Some arbitrary initial state on will evolve over some time into . Under some mild assumptions, tracing out the environment will leave you with something looking like where basically all of the finer details of the system have been coarse-grained into the parameter.
