Thermodynamically consistent approach to structure formation from first principles

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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.