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In standard nucleation theory, the nucleation process is characterized by computing $DeltaOmega(V)$, the reversible work required to form a cluster of volume $V$ of the stable phase inside the metastable mother phase. However, other quantities besides the volume could play a role in the free energy of cluster formation, and this will in turn affect the nucleation barrier and the shape of the nucleus. Here we exploit our recently introduced mesoscopic theory of nucleation to compute the free energy cost of a nearly-spherical cluster of volume $V$ and a fluctuating surface area $A$, whereby the maximum of $DeltaOmega(V)$ is replaced by a saddle point in $DeltaOmega(V,A)$. Compared to the simpler theory based on volume only, the barrier height of $DeltaOmega(V,A)$ at the transition state is systematically larger by a few $k_BT$. More importantly, we show that, depending on the physical situation, the most probable shape of the nucleus may be highly non spherical, even when the surface tension and stiffness of the model are isotropic. Interestingly, these shape fluctuations do not influence or modify the standard Classical Nucleation Theory manner of extracting the interface tension from the logarithm of the nucleation rate near coexistence.
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Macroscopic models of nucleation provide powerful tools for understanding activated phase transition processes. These models do not provide atomistic insights and can thus sometime lack material-specific descriptions. Here we provide a comprehensive framework for constructing a continuum picture from an atomistic simulation of homogeneous nucleation. We use this framework to determine the shape of the equilibrium solid nucleus that forms inside bulk liquid for a Lennard-Jones potential. From this shape, we then extract the anisotropy of the solid-liquid interfacial free energy, by performing a reverse Wulff construction in the space of spherical harmonic expansions. We find that the shape of the nucleus is nearly spherical and that its anisotropy can be perfectly described using classical models.
Recent experiments have shown how nematically-ordered tactoid shaped actin droplets can be reorganized and divided by the action of myosin molecular motors. In this paper, we consider how similar morphological changes can potentially be achieved under equilibrium conditions. Using simulations, both atomistic and continuum, and a phenomenological model, we explore how the nucleation dynamics, shape changes, and the final steady state of a nematic tactoid droplet can be modified by interactions with model adhesive colloids that mimic a myosin motor cluster. Our results provide a prescription for the minimal conditions required to stabilize tactoid reorganization and division in an equilibrium colloidal-nematic setting.
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics approach, these states have been the subject of several theoretical investigations, both analytic and numerical. The macroscopic fluctuation theory, based on a formula for the probability of joint space-time fluctuations of thermodynamic variables and currents, provides a unified macroscopic treatment of such states for driven diffusive systems. We give a detailed review of this theory including its main predictions and most relevant applications.
Here we present a model for a small system combined with an explicit entropy bath that is comparably small. The dynamics of the model is defined by a simple matrix, M. Each row of M corresponds to a macrostate of the system, e.g. net alignment, while the elements in the row represent microstates. The constant number of elements in each row ensures constant entropy, which allows reversible fluctuations, similar to information theory where a constant number of bits allows reversible computations. Many elements in M come from the microstates of the system, but many others come from the bath. Bypassing the bath states yields fluctuations that exhibit standard white noise; whereas with bath states the power spectral density varies as S(f)~1/f over a wide range of frequencies, f. Thus, the explicit entropy bath is the mechanism of 1/f noise in this model. Both forms of the model match Crooks fluctuation theorem exactly, indicating that the theorem applies not only to infinite reservoirs, but also to finite-sized baths. The model is used to analyze measurements of 1/f-like noise from a sub-micron tunnel junction.
Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly discovered fluctuation relations that hold without time-reversal symmetry, in particular, in the presence of an external magnetic field. One family of relations connects non-linear transport coefficients in the opposite magnetic fields. Another family relates currents and noises at a fixed direction of the magnetic field in chiral systems, such as the edges of some quantum Hall liquids. We review the recent experimental and theoretical research, including the controversy on the microreversibility without time-reversal symmetry, consider the applications of fluctuation theorems to the physics of topological states of matter, and discuss open problems.
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