We derive thermodynamic feasibility bounds for feedback control by combining the data-rate theorem with Landauer’s principle. For fixed-rate digital control, stabilization requires that the sum of positive Lyapunov exponents be less than the available write power divided by kBTln⁡2k_B T \ln 2kBTln2. However, complex high-dimensional controllers can circumvent this bound through two mechanisms: (1) analog coupling that reduces effective instability without writing bits, and (2) event-triggered control that achieves sparse average write rates Rˉ≪Rfixed\bar{R} \ll R_{\text{fixed}}Rˉ≪Rfixed by intervening only when the system state crosses decision boundaries. Near critical points, susceptibility amplifies weak inputs, further reducing the required intervention rate. This creates a feasibility advantage: complex controllers can stabilize plants that exceed the fixed-rate Landauer bound. The framework predicts temperature-dependent performance limits, bursty heavy-tailed intervention patterns, and critical-regime sparsity—signatures absent from conventional control theory. We propose experiments in robotic flapping flight and show how biological systems may exploit event-triggered dynamics at critical operating points to achieve control performance beyond what fixed-rate digital architectures can thermodynamically afford. Keywords: Landauer principle, event-triggered control, criticality, thermodynamic limits, high-dimensional systems, biological control