The Work Capacity of Channels with Memory - Maximum Extractable Work in Percept-Action Loops

year:2025/04
paper: https://arxiv.org/pdf/2504.06209
website:
code:
connections: thermodynamics, active inference, entropy regularization, prediction

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Tldr

In systems where actions influence future observations, maximizing prediction accuracy is thermodynamically inefficient. Optimal agents balance prediction $H(S_t|M_t)$ against action entropy $H(A_t|M_t)$.

Work capacity

In thermodynamic systems, information processing costs energy (Landauer’s principle), but clever designs can extract more than they spend. When a system transitions from uncertain to certain states (like observing a random percept become definite), this entropy reduction can be coupled to physical processes that extract work - similar to Maxwell’s demon using information about molecules to create useful energy gradients. Knowing what’s coming allows efficient energy harvest when it arrives.

Work capacity measures the maximum net energy extraction rate from a percept-action loop:

$$W=⟨H(A_t|M_t)-H(S_t|M_t){⟩}_t$$

where $A_t$ are actions, $S_t$ are percepts, $M_t$ is agent memory. Energy comes from:

• $H(S_t|M_t)$: Uncertainty about percepts - lower uncertainty (better prediction) enables more work extraction from observing surprises
• $H(A_t|M_t)$: Action randomness - higher entropy provides “erasure work” from resetting correlations

The fundamental trade-off

Perfect prediction requires remembering past actions. But remembering actions reduces $H(A_t|M_t)$, limiting work extraction. In environments with feedback, the two design principles for energy-efficient agents become incompatible:

• Maximize predictive power: Remember everything to minimize $H(S_t|M_t)$
• Forget past actions: Maximize $H(A_t|M_t)$ for thermodynamic work

Passive observation systems don’t face this trade-off. Only active systems do.

This challenges frameworks like the Free Energy Principle, predictive coding, and active inference that assume minimizing prediction error is always beneficial. For systems that act, thermodynamic efficiency requires maintaining behavioral diversity even at the cost of prediction accuracy.

Interpretation

This thermodynamic trade-off exemplifies the strong version of Goodhart’s law: optimizing prediction too hard destroys the very efficiency you seek. Similar to Kenneth Stanley’s novelty search showing that abandoning objectives often finds better solutions, this paper proves that perfect prediction is thermodynamically counterproductive in active systems.