Thermodynamic Limits of Physical Intelligence

Modern AI systems achieve remarkable capabilities at the cost of substantial energy consumption. To connect intelligence to physical efficiency, we propose two complementary bits-per-joule metrics under explicit accounting conventions: (1) Thermodynamic Epiplexity per Joule – bits of structural information about a theoretical environment-instance variable newly encoded in an agent’s internal state per unit measured energy within a stated boundary – and (2) Empowerment per Joule – the embodied sensorimotor channel capacity (control information) per expected energetic cost over a fixed horizon. These provide two axes of physical intelligence: recognition (model-building) vs.control (action influence). Drawing on stochastic thermodynamics, we show how a Landauer-scale closed-cycle benchmark for epiplexity acquisition follows as a corollary of a standard thermodynamic-learning inequality under explicit subsystem assumptions, and we clarify how Landauer-scaled costs act as closed-cycle benchmarks under explicit reset/reuse and boundary-closure assumptions; conversely, we give a simple decoupling construction showing that without such assumptions – and without charging for externally prepared low-entropy resources (e.g.fresh memory) crossing the boundary – information gain and in-boundary dissipation need not be tightly linked. For empirical settings where the latent structure variable is unavailable, we align the operational notion of epiplexity with compute-bounded MDL epiplexity and recommend reporting MDL-epiplexity / compression-gain surrogates as companions. Finally, we propose a unified efficiency framework that reports both metrics together with a minimal checklist of boundary/energy accounting, coarse-graining/noise, horizon/reset, and cost conventions to reduce ambiguity and support consistent bits-per-joule comparisons, and we sketch connections to energy-adjusted scaling analyses.

💡 Research Summary

The paper tackles the pressing issue that modern AI systems, while achieving impressive capabilities, consume massive amounts of energy. To bridge intelligence and physical efficiency, the authors introduce a two‑axis reporting framework that quantifies (i) how much structural knowledge an agent learns per unit of energy (Thermodynamic Epiplexity per Joule) and (ii) how efficiently an embodied agent can influence its environment per unit of energy (Empowerment per Joule). Both metrics are expressed in bits per joule, but they capture distinct aspects: recognition/model‑building versus control/action influence.

The authors begin by formalizing energy accounting. Measured consumption inside a clearly defined boundary, (E_{\text{cons}}), is distinguished from thermodynamic heat dissipation, (Q_{\text{diss}}). An energy‑balance equation (Eq. 1) includes internal‑energy change, exported work, and stored energy terms, and the paper stresses that any “fresh low‑entropy resources” (e.g., newly initialized memory) must be included inside the boundary if one wishes to compare against Landauer‑scale benchmarks.

Thermodynamic Epiplexity is defined as the mutual information between the agent’s internal state (W) and a latent environment variable (Z): (I(W;Z)). The amount learned in a single episode is the conditional mutual information (\Delta I = I(W_{\text{post}};Z \mid W_{\text{pre}})). For continuous variables a coarse‑graining (\epsilon) is applied. The efficiency (\eta_E) is then (\Delta I / E_{\text{cons}}) (bits per joule). By invoking the Goldt‑Seifert thermodynamic learning inequality (Lemma 1) and the data‑processing inequality, the authors derive an upper bound on (\Delta I) that involves the system’s entropy change (\Delta S_{\text{sys}}) and heat dissipation:

\