Interfacial thermodynamics has deep ramifications in understanding the boundary conditions of transport theories. We present a formulation of local equilibrium for interfaces that extends the thermodynamics of the "dividing surface," as introduced by Gibbs, to nonequilibrium settings such as evaporation or condensation. By identifying the precise position of the dividing surface in the interfacial region with a gauge degree of freedom, we exploit gauge-invariance requirements to consistently define the intensive variables for the interface. The model is verified under stringent conditions by employing high-precision nonequilibrium molecular-dynamics simulations of a coexisting vapor-liquid Lennard-Jones fluid. We conclude that the interfacial temperature is determined using the surface tension as a "thermometer," and it can be significantly different from the temperatures of the adjacent phases. Our findings lay foundations for nonequilibrium interfacial thermodynamics.

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We present a novel approach to nucleation processes based on the GENERIC framework (general equation for the nonequilibrium reversible-irreversible coupling). Solely based on the GENERIC structure of time-evolution equations and thermodynamic consistency arguments of exchange processes between a metastable phase and a nucleating phase, we derive the fundamental dynamics for this phenomenon, based on continuous Fokker-Planck equations. We are readily able to treat non-isothermal nucleation even when the nucleating cores cannot be attributed intensive thermodynamic properties. In addition, we capture the dynamics of the time-dependent metastable phase being continuously expelled from the nucleating phase, and keep rigorous track of the volume corrections to the dynamics. Within our framework the definition of a thermodynamic nuclei temperature is manifest. For the special case of nucleation of a gas phase towards its vapor-liquid coexistence, we illustrate that our approach is capable of reproducing recent literature results obtained by more microscopic considerations for the suppression of the nucleation rate due to nonisothermal effects.

In this work we show that the standard method to obtain nucleation rate-predictions with the aid of atomistic Monte-Carlo simulations leads to nucleation rate predictions that deviate 3 − 5 orders of magnitude from the recent brute-force molecular dynamics simulations [J. Diemand, R. Angélil, K. K. Tanaka, and H. Tanaka, J. Chem. Phys. 139, 074309 (2013)] conducted in the experimental accessible supersaturation regime for Lennard-Jones argon. We argue that this is due to the truncated state space literature mostly relies on, where the number of atoms in a nucleus is considered the only relevant order parameter. We here formulate the nonequilibrium statistical mechanics of nucleation in an extended state space, where the internal energy and momentum of the nuclei is additionally incorporated. We show that the extended model explains the lack in agreement between the molecular dynamics simulations by Diemand et al. and the truncated state space. We demonstrate additional benefits of using the extended state space; in particular, the definition of a nucleus temperature arrises very naturally and can be shown without further approximation to obey the fluctuation law of McGraw and Laviolette. In addition, we illustrate that our theory conveniently allows to extend existing theories to richer sets of order parameters.

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