Contemporarybiocomputingoftenapproachesbrainorganoidsasallopoieticsub-strates for logical processing, neglecting the existential imperatives that drive biolog-ical cognition. This paper proposes a fundamental paradigm shift from AllopoieticComputing toward Autopoietic Computing, grounding the emergence of sentiencein the thermodynamic necessity of survival. By integrating the Mortal Computingparadigm, where computational software is physically indissociable from its degrad-able biological hardware, with the causal hierarchy of consciousness proposed byBennett et al., we investigate the theoretical and computational feasibility of sen-tience as a recursive strategy for energy optimization. We developed and analyzeda high fidelity digital twin of an Autopoietic Chamber using the Brian2 simulator,implementing a virtual metabolism where neural activity directly regulates nutrientaccess. Our simulation results demonstrate a clear progression from the entropiccollapse of reactive matter, Stage 0, to the stabilization of phenomenal, Stage 1, so-cial, Stage 2, and narrative, Stage 3, functional identities. These findings provide apredictive proof of concept indicating that each higher order of consciousness acts asa thermodynamic filter, minimizing metabolic dissipation through increasingly com-plex causal modeling. We argue that sentience is not a byproduct of complexity buta necessary compromise with thermodynamic economy, providing a new empiricaland computational roadmap for the science of consciousness and the developmentof mortal, sentient artificial agents.