  We assume that a system at a mesoscopic scale is described by a field
$\phi(x,t)$ that evolves by a Langevin equation with a white noise whose
intensity is controlled by a parameter $1/\sqrt{\Omega}$. The system stationary
state distribution in the small noise limit ($\Omega\rightarrow\infty$) is of
the form $P_{st}[\phi]\simeq\exp(-\Omega V_0[\phi])$ where $V_0[\phi]$ is
called the {\it quasipotential}. $V_0$ is the unknown of a Hamilton-Jacobi
equation. Therefore, $V_0$ can be written as an action computed along a path
that is the solution from Hamilton's equation that typically cannot be solved
explicitly. This paper presents a theoretical scheme that builds a suitable
canonical transformation that permits us to do such integration by deforming
the original path into a straight line. We show that this can be done when a
set of conditions on the canonical transformation and the model's dynamics are
fulfilled. In such cases, we can get the quasipotential algebraically. We apply
the scheme to several one-dimensional nonequilibrium models as the diffusive
and reaction-diffusion systems.
