The relaxation dynamics of a mixed spin-1/2 and spin-1 ferrimagnetic Ising system with random anisotropy has been investigated using Onsager's theory of irreversible thermodynamics. The magnetic Gibbs energy production, arising due to irreversible processes, is computed using the equilibrium mean-field Gibbs energy, based on the variational principle and the Gibbs-Bogoliubov inequality. In the framework of linear response theory, the time derivatives of the sublattice magnetizations are treated as fluxes conjugate to their corresponding generalized forces. Two relaxation times are computed, and their dependence on temperature and crystal field variances is examined near phase transition points for four distinct topologies, each corresponding to different phase diagrams. These phase diagrams emerge from random anisotropy drawn from a bimodal probability distribution: P(Delta i)=12 delta(Delta i-Delta(1+alpha))+delta(Delta i-Delta(1-alpha)).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ P(\Delta _{i}) = \frac{1}{2}\left[ \delta (\Delta _{i} - \Delta (1+\alpha )) + \delta (\Delta _{i} - \Delta (1-\alpha ))\right] . $$\end{document} One of the relaxation times, denoted as tau 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _1$$\end{document}, increases rapidly and diverges near the critical and tricritical points separating the ferrimagnetic and paramagnetic phases. For alpha >= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \ge 0$$\end{document}, critical slowing down, characterized by the divergence of tau 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _1$$\end{document}, is observed near the isolated ordered critical points between the ferrimagnetic and disorder-induced ferrimagnetic phases. Finally, the variance of the relaxation times is analyzed across regions of crystal field and temperature, as well as the values of alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} at which re-entrant phenomena occur, due to the competing interactions in the random system.
