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随着相互作用的强度而增长。这让人怀疑MF理论是否明智地描述了强相互作用系统的物理行为。特别是，现有的忽略关联效应的卡恩-希利亚德理论的热力学一致性是值得怀疑的，这些理论大多是唯象的，即使对于时间可逆系统(即那些遵守详细平衡的系统)也是如此。最近，一种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，这些概念上的不一致可以直接追溯到忽略了粒子之间的关联，这反过来又对强耦合条件下的相变产生了深远的影响。此外，竞争局部相互作用引起的挫折效应通常很重要，但理论上只能从现象上解释，但还不能以与微观热力学和动力学相一致的方式解释。此外，粗化最终发生在微观上可逆的系统中，并产生与自由能最小值相对应的单一跨域结构。因此，在平衡系统中，稳定的模式(即局域态)通常是不可能的。然而，在非平衡条件下，可能会出现稳定的模式，例如，在考虑系统边界物质通量的所谓“对流Cahn-Hilliard”模型中，或在依赖于两个Cahn-Hilliard模型之间非互易相互作用的“主动Cahn-Hilliard”理论中。这些模型可以描述远离平衡的现象，捕捉不同的初级不稳定性，并显示丰富的相行为，但通常是现象学构造的，热力学上不一定一致。此外，新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集特别重要。尽管取得了所有进展，但热力学上一致的理论仍然难以预测非平衡结构是如何从微观原理(考虑到粒子关联)中出现的。因此，相分离和结构形成的现象学及其在中等和强相互作用极限下的非平衡热力学在很大程度上仍然没有被探索，反过来也很少被理解。此外，在非互易的“活动标量场论”中，动力学的时间可逆性经常被临时打破，因此可能不是热力学上的一致的，这有望严重影响结构的形成而脱离平衡。非反应模式形成体系的热力学一致性理论的表述和新出现的非平衡(稳定和漂移)状态的“热力学成本”的量化将是这一提议的核心。

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.