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Organisms are nonequilibrium, stationary systems self-organized via spontaneous symmetry breaking and undergoing metabolic cycles with broken detailed balance in the environment. The thermodynamic free-energy principle describes an organism's homeostasis as the regulation of biochemical work constrained by the physical free-energy cost. In contrast, recent research in neuroscience and theoretical biology explains a higher organism's homeostasis and allostasis as Bayesian inference facilitated by the informational free energy. As an integrated approach to living systems, this study presents a free-energy minimization theory overarching the essential features of both the thermodynamic and neuroscientific free-energy principles. Our results reveal that the perception and action of animals result from active inference entailed by free-energy minimization in the brain, and the brain operates as Schr{ö}dinger's machine conducting the neural mechanics of minimizing sensory uncertainty. A parsimonious model suggests that the Bayesian brain develops the optimal trajectories in neural manifolds and induces a dynamic bifurcation between neural attractors in the process of active inference.