Quasipotentials in the Nonequilibrium Stationary States or a method to get explicit solutions of Hamilton-Jacobi equations Garrido Galera, Pedro Luis We acknowledge financial support from the Spanish ”Ministerio de Ciencia e Innovaci´on” and the ”Agencia Estatal de Investigaci´on (AEI)” under Project Ref. PID2020-113681GBI00 as well as the Consejer´ıa de Conocimiento, Investigaci´on Universidad, Junta de Andaluc ´ıa and European Regional Development Fund, Ref. A-FQM-175-UGR18 and in part by AFOSR [grant FA-9550-16-1-0037]. 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/root Omega. The system stationary state distribution in the small noise limit (Omega -> infinity) is of the form P-st [phi] similar or equal to exp(-Omega V-0[phi]), where V-0[phi] is called the 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 and including some weights along with it. We get the functional form of such weights through conditions on the existence and structure of the canonical transformation. We apply the scheme to get the quasipotential algebraically for several one-dimensional nonequilibrium models as the diffusive and reaction-diffusion systems. 2021-12-16T13:33:30Z 2021-12-16T13:33:30Z 2021-11-04 info:eu-repo/semantics/article Published version: P L Garrido J. Stat. Mech. (2021) 113206. [10.1088/1742-5468/ac382d] http://hdl.handle.net/10481/72100 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Institute of Physics