The High Cost of Thinking: From the Quantum Szilard Engine to the Thermodynamic Limits of Artificial Intelligence

Information is physical. Here, we validate Rolf Landauer's principle (E_erase >= k_B T ln 2) through a unitary simulation of a Quantum Szilard Engine, demonstrating that the entropy reduction achieved by a Maxwell's Demon is exactly balanced by the energy cost of memory erasure. We apply this fundamental bound to audit state-of-the-art Artificial Intelligence training protocols. Our results reveal a "Landauer Gap" of ~10^8 in current CMOS architectures. We argue that the exponential scaling of AI is physically unsustainable with irreversible logic, identifying reversible quantum computing not merely as a speed advantage, but as a thermodynamic necessity.