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Statistical mechanics, first developed for equilibrium systems, stands as one of physics' greatest triumphs. Living systems, however, operate far from equilibrium, processing information and responding to signals in ways that challenge traditional equilibrium frameworks. We demonstrate that by shifting focus from state distributions to complete stochastic trajectories, we can extend the success of statistical physics to non-equilibrium biological systems. Our trajectory-based approach reveals that these systems encode more information than previously recognized, enabling phenomena like multiplexed sensing through single molecular pathways. We develop universal theoretical tools - integrating information theory and response theory - that hold arbitrarily far from equilibrium, uncovering fundamental principles governing how biological systems sense and respond to their environment. These insights not only explain existing biological designs but also provide quantitative guidelines for engineering synthetic molecular systems. Our work bridges the gap between equilibrium statistical physics and the dynamic complexity of living matter, establishing design principles for biological information processing.