expression of the Second Law of Thermodynamics. Since the vacuum is the most elementary system, all order parameters should have sharp values in this state. This is expressed by the weak mixing property: $$\label{weakmixing}
\lim_{T \rightarrow \infty}
\frac{\mbox{\footnotesize $1$}}{\mbox{\footnotesize $T$}}
\int_0^T  \, \left( \omega( A(t) B)  -  
\omega(A(t))\, \omega(B) \right) \, dt = 0 \, ,$$ for all $A,B \in {{\cal A}}$, where $A(t) \doteq e^{\, itM } A e^{\, -itM }$. The restriction of the state $\omega$ to $\As(W)$ is said to be central if $\omega(AB) = \omega(BA)$, for all $A,B \in \As(W)$. If this holds, then either $\Omega$ is annihilated by most of the observables in $\As(W)$ or $\As(W)$ is a finite algebra (cf. Section 8.1 in [@KadRing]). In quantum field theory this is a physically pathological circumstance, which we shall exclude from consideration.

These basic features of the vacuum can be summarized as follows.

\(iv) The vacuum vector $\Omega$ is cyclic for $\As$ and determines a passive, weakly mixing and noncentral state $\omega$ for all geodesic and all uniformly accelerated observers.

The Standing Assumptions (i)–(iv) are model–independent and physically natural. In this paper we shall show that these assumptions entail that for geodesic observers the vacuum $\omega$ 