Haueis and Colaço argue that metabolic constraints are fundamental and underutilized in cognitive modeling. We agree but argue that the theoretical implications of their view go far beyond this insight. We propose that under three minimal assumptions – (i) that the brain admits an approximately informationally closed, Markovian description at an appropriate spatiotemporal scale; (ii) that its dynamics can be expressed in terms of variational free energy; and (iii) that cognitive behavior reflects the algorithmic expression of the brain’s interaction with its environment – accounting for metabolic constraints entails a stronger conclusion: cognition can be formalized as a generative, control-theoretic process bounded by energy-dependent limits on controllability.

This follows directly from converging results in cybernetics and statistical physics that establish a link between energy dissipation, information processing, and regulation. While metabolism in the target article often refers to the biological implementation of energy transformations, we argue that its constraints arise from general thermodynamic principles governing nonequilibrium systems.

We begin from a minimal physical characterization of the brain as a nonequilibrium system maintaining organization against entropic decay (Prigogine, Reference Prigogine1978). Survival, therefore, depends on regulating internal states within bounded ranges despite external perturbations. By the Good Regulator Theorem (Conant & Ross Ashby, Reference Conant and Ross Ashby1970), any system capable of effective regulation must embody a model of the variables it regulates. If the brain must regulate its metabolic exchanges to remain within viability constraints, it must instantiate an internal model of those dynamics. This extends beyond the evaluative role proposed by Haueis and Colaço: energy-constrained cognition is necessarily model-based, even when implemented through physical dynamics rather than explicit computation (Haimerl, Rodrigues, & Paton, Reference Haimerl, Rodrigues and Paton2025).

A formal expression of this requirement is provided by the free energy principle (Friston, Reference Friston2009), which characterizes self-organizing systems that resist entropy. Within this framework, the system minimizes variational free energy:

$$F = {\mathbb{E}_{q\left( \phi \right)}}\left[ {{\rm{ln}}q\left( \phi \right) - {\rm{ln}}p\left( {o,\phi } \right)} \right] = \underbrace {{D_{KL}}\left[ {q\left( \phi \right)\parallel p\left( \phi \right)} \right]}_{complexity} - \underbrace {{\mathbb{E}_{q\left( \phi \right)}}\left[ {{\rm{ln}}p\left( {o\mid \phi } \right)} \right]}_{accuracy}$$

Here, $\phi $ denotes latent (hidden) states and $o$ observations. Crucially, the complexity term – representing the divergence between the variational posterior and the prior – is not merely informational. When inference is physically implemented, updating internal states is expected to incur thermodynamic cost, and recent work has begun to make this link explicit (Fields, Goldstein, & Sandved-Smith, Reference Fields, Goldstein and Sandved-Smith2024). Landauer’s principle establishes a lower bound on dissipation for logically irreversible operations (Landauer, Reference Landauer1961). More generally, results from stochastic thermodynamics show that maintaining nonequilibrium distributions requires continuous dissipation, with lower bounds related to their divergence from equilibrium (Horowitz & England, Reference Horowitz and England2017; Sanders, Baldovin, & Muratore-Ginanneschi, Reference Sanders, Baldovin and Muratore-Ginanneschi2024). In this sense, inference is not purely abstract computation, but a physically instantiated process constrained by thermodynamic cost.

A complementary control-theoretic formulation makes this constraint clearer. Let $w_{ij}^0$ denote passive transition rates and $w_{ij}^\pi $ the transition rates under a control policy $\pi $ . The energetic cost of imposing controlled dynamics over trajectories $\tau $ can be written as ${\rm{Cost}}\left( \pi \right) = {D_{KL}}\left( {p\left( {\tau \mid \pi } \right)\parallel {{\rm{p}}_0}\left( \tau \right)} \right) = \sum\limits_\tau p \left( {\tau \mid \pi } \right){\mkern 1mu} {\mkern 1mu} {\rm{ln}}\;{\mkern 1mu} {{p\left( {\tau \mid \pi } \right)} \over {{p_0}\left( \tau \right)}}$ . This expression shows that control cost arises from biasing controlled trajectories away from passive dynamics, thereby reshaping probability flow over state space (Kawakita et al., Reference Kawakita, Kamiya, Sasai, Kitazono and Oizumi2022). Available energy, therefore, defines a control budget that constrains reachable distributions, admissible transition structure, and the directional organization of dynamics. In neuroscience, this broader intuition is consistent with work linking controllability-related quantities to brain structural properties (Haimerl et al., Reference Haimerl, Rodrigues and Paton2025; Jamalabadi et al., Reference Jamalabadi, Zuberer, Kumar, Li, Alizadeh, Amani, Gaser, Esterman and Walter2021; Takagi, Reference Takagi2021). In cognitive and psychiatric settings, it is also consistent with recent proposals that energetic constraints help shape the effective landscape over which cognition evolves (Kheirkhah et al., Reference Kheirkhah, Shariatpanahi, Hahn, Tiruvadi, Koppe, Nozari, Hofmann and Jamalabadi2026; Markman & Otto, Reference Markman and Otto2011). At the same time, energetic resources do not by themselves determine dynamics: the set of achievable states depends jointly on energy and system structure, including the geometry of the state space and the topology of passive transitions. Sustaining a nonequilibrium distribution, therefore, requires ongoing dissipation, linking energetic cost to the persistence of structured behavior (Horowitz & England, Reference Horowitz and England2017). Energy thus constrains controllability without overriding structural limitations, implying that cognitive dynamics arise from the interaction between energetic resources and intrinsic system organization. Under these conditions, metabolic regulation naturally entails generative inference, insofar as agents must predict and selectively sample data so as to maintain their structural integrity (Sajid et al., Reference Sajid, Ball, Parr and Friston2021).

Importantly, the validity of this framework depends on the spatiotemporal scale at which its assumptions remain a reasonable approximation. Formal treatments of control cost and causal structure are typically developed for Markovian systems, while informational closure provides an additional criterion for identifying scales at which variables behave as partially autonomous dynamical descriptions (Bertschinger et al., Reference Bertschinger, Olbrich, Ay and Jost2008; Hoel, Albantakis, & Tononi, Reference Hoel, Albantakis and Tononi2013). These conditions are unlikely to hold uniformly across scales, but may be approximately satisfied at microscopic or mesoscopic levels of neural organization. At the same time, cognitive variables of interest are usually defined at more macroscopic and behaviorally interpretable levels (Jazayeri & Afraz, Reference Jazayeri and Afraz2017), creating tension if closure weakens at these levels. Thus, our framework is empirically testable: by combining metabolic measures with neural and behavioral data across tasks that vary in control cost, one can test at which scales energy expenditure, state transitions, and performance covary in line with model predictions.

Taken together, from this framework, three main insights arise: (i) Progress in cognitive modeling will not come from assigning metabolic costs to isolated cognitive operations, but from identifying mesoscopic variables that exhibit approximate dynamical autonomy and modeling their evolution as generative processes under energetic constraints. (ii) Optimality of cognition is not sufficiently defined by accuracy alone, but by the best achievable inference or control under given energetic resources. Metabolic constraints, therefore, do not merely prune the space of admissible models; they shape the effective geometry of reachable trajectories in state space. Cognition, in this sense, is not an unconstrained accuracy-maximizing engine, but a resource-bounded controller of probability flow, whose feasible trajectories are limited jointly by energetic budget and system structure. (iii) Efficient cognitive agents – whether biological or artificial – are intrinsically energy-constrained generative controllers, with explicit costs on deviations from default dynamics. Efficient architecture aligns desired behaviors with low-cost trajectories, leveraging structured representations and selective computation, essentially redefining optimality as performance maximization under the hard physical limits of energy and resource constraints.