>[!warning] >This content has not been peer reviewed. # Thermodynamics and Landauer — RRT foundation Classical **thermodynamics** and the **Landauer principle** (minimum cost to erase a bit: $k_B T \ln 2$) are the second foundational area for mapping physics into RRT. They fix the **cost of persistence** and the meaning of "noise" in the Resource Triangle. --- ## I. Classical side - **Landauer (1961):** Irreversibility and heat generation in the computing process; minimum energy to erase one bit = $k_B T \ln 2$. - **Thermodynamics:** Persistence in a thermal environment ($T > 0$) requires active expenditure; entropy and temperature set the scale of the "noise" the system works against. --- ## II. Mapping to RRT / RST | Concept | RRT / RST identity | Axiom / equation | |:---|:---|:---| | **Noise ($T$)** | Environmental thermal / expansion scale the substrate works against. | A2, A3; $N$ in the triangle. | | **Minimum power** | $\Phi_{\min} = k_B \ln 2 \sum_i \frac{d_i \cdot \sigma_i \cdot T_i}{\tau_i}$ — Relational Landauer Principle. | RRT draft; Landauer floor. | | **Persistence** | Maintaining resolution $\sigma$ against noise; identity is dissipative. | A2 (Resolution), A3 (Translation). | | **Efficiency** | $K_R = \Phi_{\mathrm{measured}} / \Phi_{\min} \ge 1$ — no system below Landauer. | RRT; universal boundary. | So: **thermodynamics** supplies the "noise" cost; **Landauer** supplies the minimum cost of maintaining a bit. Together they underpin why the triangle splits effort between signal and noise and why $\mu$ cannot exceed 1. --- ## Links - **Foundation index:** [[../Foundation index]] - **RRT axioms:** [[Relational Resolution Theory (RRT)]] - **Applications Roadmap:** [[../../Applications Roadmap]]