średnia statystyczna

Thus the expectation value of energy is also time independent.

The situation in quantum field theory is rather different: the expectation value of the energy density can be negative at any given point.

The time-dependence of the expectation value does not depend on this choice, however.

In these cases, the expectation value is determined only by the more general formula (6).

A precise definition of this expectation value is given below.

The expectation values are with respect to the bath degrees of freedom.

In general we must understand the expectation value of an observable A as a statistical mean.

Thus both have infinite expectation values, and hence so must "X" too.

What would the expectation value of the mutual information be?

That is we always want the expectation value of the normal ordered product to be zero.