  Multistability of mesoscopic, driven biochemical reaction systems has
implications to a wide range of cellular processes. Using several simple
models, we show that one class of bistable chemical systems has a deterministic
counterpart in the nonlinear dynamics based on the Law of Mass Action, while
another class, widely known as noise-induced stochastic bistability, does not.
Observing the system's volume ($V$) playing a similar role as the inverse
temperature ($\beta$) in classical rate theory, an van't Hoff-Arrhenius like
analysis is introduced. In one-dimensional systems, a transition rate between
two states, represented in terms of a barrier in the landscape for the dynamics
$\Phi(x,V)$, $k\propto\exp\{-V\Delta\Phi^{\ddag}(V)\}$, can be understood from
a decomposition $\Delta\Phi^{\ddag}(V) \approx\Delta\phi_0^{\ddag}
\Delta\phi_1^{\ddag}/V$. Nonlinear bistability means $\Delta\phi_0^{\ddag}>0$
while stochastic bistability has $\Delta\phi_0^{\ddag}<0$ but
$\Delta\phi_1^{\ddag}>0$. Stochastic bistabilities can be viewed as remants (or
"ghosts) of nonlinear bifurcations or extinction phenomenon, and
$\Delta\phi_0^{\ddag}$ and $\Delta\phi_1^{\ddag}$ as "enthalpic" and "entropic"
barriers to a transition.
