Thermodynamically consistent approach to structure formation from first principles

从第一原理出发的结构形成的热力学一致方法

• 批准号: 519908559
• 负责人: Dr. Aljaz Godec
• 金额: --
• 依托单位: Max-Planck-Institut für Multidisziplinäre Naturwissenschaften
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/519908559?language=en
• 关键词: Thermodynamically; consistent; approach; structure; formation

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.

我们对集体现象的理解，特别是在非均匀系统中，主要是基于平均场思想，忽视了相关性，其重要性反过来随着相互作用的强度而增加。这就引起了人们对MF思想是否合理地描述了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，Cahn-Hilliard理论忽略相关效应的热力学一致性是值得怀疑的，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，从第一原理出发的物理一致的方法揭示了概念上的不一致，可以直接追溯到忽略粒子之间的相关性，这反过来又对强耦合下的相变产生了深远的影响。此外，由于竞争的本地相互作用的挫折效应往往是重要的，但理论上只占现象学，但尚未在微观热统计学和动力学一致的方式。此外，粗化最终发生在微观可逆系统中，并产生对应于自由能最小值的单个跨域结构。因此，稳定的模式（即局域态）在平衡系统中通常是不可能的。然而，在非平衡条件下可能会出现稳定的模式，例如，在所谓的“对流Cahn-Hilliard”模型中，该模型考虑了系统边界上的物质通量，或者在“主动Cahn-Hilliard”理论中，该理论依赖于两个Cahn-Hilliard模型之间的非互易相互作用。这些模型可以描述远离平衡态的现象，捕捉不同的初级不稳定性，并显示丰富的相行为，但通常是唯象构造的，在理论上不一定是一致的。此外，新兴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是特别重要的酶集群。尽管取得了所有的进展，一个理论上一致的理论，将预测如何非平衡结构出现的微观原则（占粒子相关性）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然未被探索，反过来也知之甚少。此外，在非互易的“有源标量场理论”中，动力学的时间可逆性经常被临时打破，因此可能不是物理上一致的，这预计会严重影响平衡态的结构形成。非反应模式形成系统的热力学一致性理论的制定和新出现的非平衡（稳定和漂移）状态的“热力学成本”的量化将是这一建议的核心。