Caregiver Burnout as Sustained Displacement Accumulation: Self-Erasure as Wrong Attractor, Compassion Fatigue as Sensor Degradation, and the Ethics of Return

We apply the Displacement Framework to caregiver burnout, formalizing it as Φ accumulation beyond a critical threshold when care demands produce repeated D(ξ_self) without adequate recovery intervals. The caregiver ground state S°_caregiver is defined as sustainable care — the capacity to provide care while maintaining one's own physical, emotional, and identity needs through sufficient reciprocity, even if asymmetric.

Nine formal propositions are derived covering: S°_caregiver as sustainable reciprocal equilibrium, uninterrupted caregiving as Φ accumulation without discharge (with a formal threshold Φ_critical), self-erasure as wrong attractor in which personal needs register as morally impermissible, guilt as an exit-barrier restoring force that prevents return to S°_caregiver, compassion fatigue as empathic sensor degradation distinct from exhaustion, moral injury as ethical displacement when institutional constraints prevent adequate care, social isolation as positive-feedback Φ amplifier through friendship attrition, respite care as D(ξ) interruption intervention, and the ethics of caregiver self-care as a sustainability condition rather than a self-indulgence.

The framework distinguishes compassion fatigue (empathic sensor damage) from simple depletion, explains why guilt is a maintenance mechanism of the wrong attractor rather than a guide to appropriate action, and addresses gendered caregiving disparities and policy implications for paid family leave and caregiver relief programs.