A free energy principle for generic quantum systems (2112.15242v1)

Abstract: The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on surprisal (a.k.a., self-information). This upper bound can be read as a Bayesian prediction error. Equivalently, its negative is a lower bound on Bayesian model evidence (a.k.a., marginal likelihood). In short, certain random dynamical systems evince a kind of self-evidencing. Here, we reformulate the FEP in the formal setting of spacetime-background free, scale-free quantum information theory. We show how generic quantum systems can be regarded as observers, which with the standard freedom of choice assumption become agents capable of assigning semantics to observational outcomes. We show how such agents minimize Bayesian prediction error in environments characterized by uncertainty, insufficient learning, and quantum contextuality. We show that in its quantum-theoretic formulation, the FEP is asymptotically equivalent to the Principle of Unitarity. Based on these results, we suggest that biological systems employ quantum coherence as a computational resource and - implicitly - as a communication resource. We summarize a number of problems for future research, particularly involving the resources required for classical communication and for detecting and responding to quantum context switches.

• The paper extends the classical free energy principle into a quantum framework by remapping Markov blankets as holographic screens for information exchange.
• It demonstrates that quantum systems operate as Bayesian agents using quantum reference frames to interact with their environment.
• The study shows that iterative minimization of prediction errors drives quantum systems toward entanglement, aligning with the principle of unitarity.

A Free Energy Principle for Generic Quantum Systems

The paper "A Free Energy Principle for Generic Quantum Systems" by Fields et al. extends the classical Free Energy Principle (FEP) into the field of quantum information theory. This work aims to explore the FEP within a quantum framework, devoid of spacetime constraints, providing implications for understanding cognitive and biological systems at quantum scales.

Reformulation of FEP in Quantum Theoretical Context

Traditionally, the FEP has been used to explain the behavior of living systems and their propensity to resist the Second Law of Thermodynamics by minimizing free energy. The principle posits that living systems act to minimize a variational free energy, which serves as an upper bound on surprisal—a measure of unexpected states. In the classical approach, this involves maintaining a Markov Blanket (MB) to differentiate between internal (self) and external (environment) states, thereby allowing systems to predict and act to minimize uncertainty.

This paper reformulates the FEP within the quantum information paradigm. A primary feat of this reformulation involves mapping the concept of MBs to holographic screens in quantum theory, which act as interaction boundaries that support information exchange. These screens symmetricize the quantum interaction dynamics, permitting sensory and active states to correspond to incoming and outgoing classical signals.

Quantum Systems as Agents

In the quantum reformulation, any system with a spacetime-independent MB can be considered an observer, with the potential for agency. The authors propose that systems inherently behave as Bayesian agents, capable of deploying quantum reference frames (QRFs) for interaction with their environment. These QRFs essentially serve as operational semantics for external states, engendering a realization of semantics through a thermodynamically costed symmetry breaking process on holographic screens.

Implications and Asymptotic Behavior

One of the significant conclusions of this paper is the asymptotic equivalence of the FEP to the Principle of Unitarity in quantum mechanics. Through iterative minimization of prediction errors by aligning QRFs across interaction boundaries, systems evolve towards entanglement with their environment rather than remaining separable entities. This indicates that, given infinite time, any quantum system following the FEP will become entangled, transforming its prediction model into a cooperative, entangled state with its environment.

This work further implies that biological systems, including their trivial quantum interactions, are driven towards states where separability from the environment diminishes. Hence, it predicts a broader scope of quantum coherence in biological processes than presently acknowledged, challenging the classical perspective of purely classical macroscopic entities.

Conclusion

Fields et al.'s paper provides a comprehensive framework where the FEP accommodates quantum theoretical principles to explore the phenomenology of information-processing systems at any scale, removing spacetime and scale constraints. The insights offered here could influence future explorations in cognitive science, proposing a unifying framework wherein systems universally behave under the FEP, analogous to unitarity, as a fundamental principle, thereby broadening the lens through which we view both physical and cognitive processes in living systems. These conceptual developments not only suggest that existing premises in quantum biology hold merit but also advocate for new experimental advances to substantiate these claims, particularly in realms that witness potential entanglement and quantum coherence phenomena.