KMS-state, $\omega_{\boldsymbol{\beta}}$ is an LTE state, with constant inverse temperature vector $\boldsymbol{\beta}$. The interesting feature of the definition of LTE states is that $\boldsymbol{\beta}(x)$ can vary with $x$ in spacetime, and the question of existence of LTE states which are not global KMS states arises. In particular, fixing the order $N$ and the spacetime region $D$, which functions $\boldsymbol{\beta}(x)$ or $\varrho_x$ can possibly occur? They surely cannot be completely arbitrary, particularly for open $D$, since the Wick-square of $\Phi_0$ and its balanced derivatives are subject to dynamical constraints which are a consequence of the equation of motion for $\Phi_0$. We put on record some of the results which have been established so far.\
[**The hot bang state**]{} [@BOR; @BuHB]\
A state of $\Phi_0$ (zero mass case) which is an LTE state with a variable, sharp inverse temperature vector field on the open forward lightcone $V_+$ was constructed in [@BOR] and further investigated in [@BuHB]. This state is called the hot bang state $\omega_{\rm HB}$, and for $x,y$ in $V_+$, its two-point function $w_{\rm HB}$ has the form $$\begin{aligned}
 \label{2pHB}
w_{\rm HB}(x,y) &= \frac{1}{(2 \pi)^{3}} \int_{\mathbb{R}^4}
     {\rm e}^{- i (x - y)^\mu p_\mu} \epsilon(p_0) \delta(p^\mu p_\mu) 
     \frac{1}{1 - {\rm e}^{- a 