Thermodynamically consistent approach to structure formation from first principles

我们对集体现象的理解，特别是在非均匀系统中，主要是基于忽略相关性的平均场思想，而相关性的重要性反过来又随着相互作用的强度而增长。这引起了人们对MF理论是否合理地描述强相互作用系统的物理行为的怀疑。特别是，现有的，主要是现象学的，忽略相关效应的卡恩-希利亚德理论的热力学一致性是值得怀疑的，即使对于时间可逆系统（即服从详细平衡的系统）也是如此。最近，从第一原理出发的热力学一致性方法揭示了概念上的不一致性，这种不一致性可以直接追溯到忽略粒子之间的相关性，而这反过来又对强耦合下的相变产生了深远的影响。此外，由于相互竞争的局部相互作用引起的挫折效应通常很重要，但理论上仅在现象学上进行了解释，但尚未以与微观热统计和动力学一致的方式进行解释。此外，粗化最终发生在微观可逆系统中，并产生与自由能最小值相对应的单畴跨越结构。因此，稳定模式（即局域状态）通常在平衡系统中是不可能的。然而，稳定模式可能在非平衡条件下出现，例如，在所谓的“对流Cahn-Hilliard”模型中，计算了跨越系统边界的物质通量，或者在“主动Cahn-Hilliard”理论中，依赖于两个Cahn-Hilliard模型之间的非互反相互作用。这些模型可以描述远离平衡的现象，捕获不同的初级不稳定性，并显示丰富的相行为，但通常是现象学上的构建，热力学上不一定一致。此外，出现的非平衡稳定和漂移状态的热力学成本仍然难以捉摸，这在生物物理背景下可能对酶聚类特别重要。尽管取得了种种进步，但预测非平衡结构如何从微观原理（考虑粒子相关性）中产生的热力学一致性理论仍然难以捉摸。因此，相分离和结构形成的现象学及其在中间和强相互作用极限下的非平衡热力学在很大程度上仍未被探索，反过来也知之甚少。此外，在非互易的“活动标量场理论”中，动力学的时间可逆性经常被临时打破，因此可能不具有热力学一致性，这将严重影响结构的形成。非反应模式形成系统的热力学一致性理论的公式和新兴非平衡状态（稳定和漂移）的“热力学成本”的量化将是本提案的核心。

Our understanding of collective phenomena, in particular in inhomogeneous systems, is mostly based on mean-field ideas that neglect correlations, whose importance in turn grows with the strength of interactions. This raises doubts whether MF ideas sensibly describe the physical behavior of strongly interacting systems. In particular, the thermodynamic consistency of existing, mostly phenomenological, Cahn-Hilliard theories that ignore correlation effects is questionable, even for time-reversible systems (i.e. those obeying detailed balance). Recently a thermodynamically consistent approach starting from first principles revealed conceptual inconsistencies that could be traced directly to the neglect of correlations between particles, which in turn has profound consequences for phase transformations at strong coupling. Moreover, frustration effects due to competing local interactions are often important yet theoretically only accounted for phenomenologically, but not yet in a manner consistent with microscopic thermostatistics and kinetics. Moreover, coarsening eventually occurs in microscopically reversible systems and yields a single domain-spanning structure that corresponds to the free energy minimum. Therefore, stable patterns (i.e. localized states) are normally not possible in equilibrium systems. However, stable patterns may emerge under non-equilibrium conditions, e.g. in the so-called “convective Cahn-Hilliard” model accounting for material flux across the system’s boundaries, or in “active Cahn-Hilliard” theories relying on non-reciprocal interactions between two Cahn-Hilliard models. These models can describe far-from-equilibrium phenomena, capture different primary instabilities, and display a rich phase behavior, but are usually constructed phenomenologically and are thermodynamically not necessarily consistent. Moreover, the thermodynamic cost of emerging non-equilibrium steady and drifting states remains elusive, which in a biophysical context may be particularly important for enzyme clustering. Notwithstanding all advances, a thermodynamically consistent theory that would predict how non-equilibrium structures emerge from microscopic principles (accounting for particle correlations) remains elusive. As a result, the phenomenology of phase separation and structure formation and its non-equilibrium thermodynamics in the intermediate and strong-interaction limit remain largely unexplored and in turn poorly understood. Moreover, time-reversibility of dynamics in non-reciprocal “active scalar field theories” is often broken ad hoc and therefore may not be thermodynamically consistent, which is expected to critically impact structure formation out of equilibrium. The formulation of a thermodynamically consistent theory of non-reactive pattern-forming systems and the quantification of the “thermodynamic cost” of emerging non-equilibrium (steady and drifting) states will be at the heart of this proposal.