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Multistability of mesoscopic, driven biochemical reaction systems hasimplications to a wide range of cellular processes. Using several simplemodels, we show that one class of bistable chemical systems has a deterministiccounterpart in the nonlinear dynamics based on the Law of Mass Action, whileanother class, widely known as noise-induced stochastic bistability, does not.Observing the system's volume ($V$) playing a similar role as the inversetemperature ($\beta$) in classical rate theory, an van't Hoff-Arrhenius likeanalysis is introduced. In one-dimensional systems, a transition rate betweentwo 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 froma 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.

van't Hoff-Arrhenius Analysis of Mesoscopic and Macroscopic Dynamics of Simple Biochemical Systems: Stochastic vs. Nonlinear Bistabilities