A free energy principle for generic quantum systems
Chris Fieldsa∗, Karl Fristonb, James F. Glazebrookc,dand Michael Levine
January 3, 2022
1 介绍翻译节选：
所有的物理系统,包括整个环境,都可以被认为是“观察者”,它们也作用于周围环境, 为随后的观察“做准备”,这种想法在量子理论中已经变得很普遍,在很大程度上取代了传统量子力学的“波函数坍缩”假设
虽然量子理论最初是作为一种特别适用于原子尺度及以下的理论发展起来的——现在仍被广泛认为——但从惠勒[24], 费因曼[25], 和Deutsch[26]的开创性工作开始，在过去的几十年里，它已经被重新表述为无尺度信息论和越来越被视为观察过程本身的理论。
对量子理论的这种更新的理解与FEP的概括非常吻合,因此,不证自明的和积极的推论,适用于所有的“事物”,如[10], 并以不确定性下的观察作为推论的一般观点。
在接下来的内容中,我们将从[10], 将 FEP 公式化为量子信息理论的一般原理。我们特别指出,在任何一个“主体”或“粒子”部署了量子参考系 (qrf)的环境中,FEP 都会自然出现,
量子参考系是一种物理系统,它赋予观测结果以可操作的语义[39,40],识别和描述其环境中其他系统的状态。
这种重新表述消除了公式中关于随机动力系统的两个中心假设[10]:时空嵌入的假设(或量子理论语言中的“背景”)和“客观”或独立于观察者的随机性的假设。
它进一步揭示了局部遍历性和系统可识别性之间的深刻关系,因此在[10],以及 物理系统之间可分性的量子理论概念 , 即不存在量子纠缠 。
因此,任何量子系统,只要能随着时间的推移从它的环境中被区分出来,就可以被认为是自组织的和自证的,如[10].
然后我们证明,当 FEP 达到一个渐近极限时,它驱使系统从可分性走向纠缠,从而走向每个“事物”和它的环境之间——观察者和被观察者之间——的超经典统计耦合。
在这种情况下,FEP 再现了幺正原理,即信息守恒原理,它同样驱使所有相互作用的系统渐近地走向纠缠。
因此,在重要的意义上,FEP 是量子理论最基本的原理——幺正原理的另一种陈述。
因此,它适用于比“事物”的直观概念更广泛的系统,例如量子场,并且原则上适用于从普朗克尺度到宇宙尺度。因此, 将 FEP 公式化为量子资讯理论的一般原则,大幅扩大了「认知」或资讯处理概念合理适用的系统范围。
2 原文：
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., selfinformation). 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.
1 Introduction
（自由能及 Markov blankets (MBs)一段论述略）
The idea that all physical systems, including the environment at large, can be considered “observers” that also act on their surroundings to “prepare” them for subsequent observations has become commonplace in quantum theory, largely replacing the “wave-function collapse” postulate of traditional quantum mechanics [15] with interaction-induced decoherence (i.e., dissipation of quantum coherence) as the generator of classical information [16, 17, 18, 19, 20].1Indeed while quantum theory was originally developed – and is still widely regarded – as a theory specifically applicable at the atomic scale and below, since the pioneering work of Wheeler [24], Feynman [25], and Deutsch [26], it has, over the past few decades, been reformulated as a scale-free information theory [27, 28, 29, 30, 31, 32] and is increasingly viewed as a theory of the process of observation itself [33, 34, 35, 36, 37, 38].
This newer understanding of quantum theory fits comfortably with the generalization of the FEP, and hence of self-evidencing and active inference, to all “things” as outlined in [10], and with the general view of observation under uncertainty as inference.
In what follows, we take the natural next step from [10], formulating the FEP as a generic principle of quantum information theory. We show, in particular, that the FEP emerges naturally in any setting in which an “agent” or “particle” deploys quantum reference frames (QRFs), namely, physical systems that give observational outcomes an operational semantics [39, 40], to identify and characterize the states of other systems in its environment.
This reformulation removes two central assumptions of the formulation in terms of random dynamical systems employed in [10]: the assumption of a spacetime embedding (or “background” in quantum-theoretic language) and the assumption of “objective” or observerindependent randomness. It further reveals a deep relationship between the ideas of local ergodicity and system identifiability, and hence the idea of “thingness” highlighted in [10], and the quantum-theoretic idea of separability, i.e., the absence of quantum entanglement, between physical systems.
Any quantum system that can be distinguished from its environment over time can, therefore, be regarded as self-organizing and self-evidencing as described in [10]. We then show that when the FEP is taken to an asymptotic limit, it drives systems away from separability towards entanglement, and hence towards a supraclassical statistical coupling between each “thing” and its environment – between the observer and the observed. In this, the FEP reproduces the Principle of Unitary, i.e. the Principle of Conservation of Information, which similarly drives all interacting systems asymptotically toward entanglement. Hence the FEP is, in an important sense, an alternative statement of the Principle of Unitarity, the most fundamental principle of quantum theory. It therefore applies to a much broader array of systems than would fall under an intuitive idea of “thingness,” e.g. to quantum fields, and applies in principle from the Planck scale to cosmological scales. Formulating the FEP as a generic principle of quantum information theory thus substantially expands the range of systems to which “cognitive” or information-processing concepts reasonably apply.
We begin by reviewing in §2 the basic principles of quantum theory from an information theoretic perspective, limiting the formalism to focus on the physical meaning of the theory.
Using the category-theoretic [41, 42] formalism of Channel Theory – developed by Barwise and Seligman [43] to formalize the operational semantics of natural languages – we develop a generic formal representation of QRFs and show how the noncommutativity of QRFs induces quantum contextuality [44, 45], a nonclassical effect demonstrating the presence of entanglement between distinct physical degrees of freedom. We develop in §3 a generic, formal description of how one quantum system identifies another quantum system as a persistent entity – a “thing” – and measures, records, and compares its states by deploying specific sequences of QRFs. This identification and measurement process depends critically on breaking thermodynamic symmetries, and therefore on system-specific flows of energy.
These sections together provide a representation of generic quantum systems as observers, or in the language of Gell-Mann and Hartle [46] “information gathering and using systems”(IGUSs), that is free of scale and spacetime embedding (i.e. “background”) dependent assumptions. It also treats all probabilities as observer-relative. We then show in §4 how the FEP emerges in this setting and analyze its asymptotic behavior; in particular, we consider how the FEP addresses the fundamental problem posed by quantum context switches. We conclude in §5 by discussing the relevance of these results to a scale-independent understanding of biological systems as “particles” that interact with other “particles,” whether these are other organisms, “objects,” or an undifferentiated environment. We consider in particular the circumstances in which this “particle” nature can break down, and suggest that well-designed experiments may be expected to detect quantum context switches or violations of the Bell [47] or Leggett-Garg [48] inequalities, any of which indicate entanglement, by macroscopic biological systems under ordinary conditions.
其余内容可以参考原论文。 https://readpaper.com/paper/4575922568536530945
