Thermodynamic Limits of Physical Intelligence
Koichi Takahashi, Yusuke Hayashi
TL;DR
This work formalizes physical intelligence through two complementary bits-per-joule metrics: Thermodynamic Epiplexity per Joule, which captures how much environmental structure is learned per unit energy, and Empowerment per Joule, which measures the embodied control capacity per energy spent. It provides a normative target via mutual information $I(W;Z)$ and an operational companion through compute-bounded MDL epiplexity, with explicit boundary, coarse-graining, horizon, and cost conventions to enable reproducible comparisons. The paper derives Landauer-scale closed-cycle benchmarks for epiplexity under boundary-closure assumptions and discusses open-boundary decoupling limits, while linking dissipation to measured energy and proposing a unified framework to report both metrics together. It also details practical reporting guidelines, estimation strategies, and connections to scaling analyses and quantum computing, arguing that thermodynamic benchmarks remain central even as hardware and algorithms evolve. The overall message is that transparent, convention-driven reporting of learning and control efficiencies is essential for meaningful bits-per-joule comparisons in physical AI systems and for understanding fundamental energy-information trade-offs in embodied intelligence.
Abstract
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.