Related papers: Continuum Free-Energy Computing
Landau theory usually treats free-energy coefficients as intrinsic parameters fixed by thermodynamic variables. We show that externally written microscale fields can survive coarse graining and enter the free-energy functional as spatially…
A variety of methods are developed for characterising the free energy landscapes of continuum, Landau-type free energy models. Using morphologies of lipid vesicles and a multistable liquid crystal device as examples, I show that the methods…
Nonlinear plasma physics problems are usually simulated through comprehensive modeling of phase space. The extreme computational cost of such simulations has motivated the development of multi-moment fluid models. However, a major challenge…
Computational studies of the thermodynamic properties of materials at the mesoscopic and macroscopic scales -- involving lengths and times of at least $\mu$m and $\mu$s, respectively -- rely on a coarse-graining approximation such that only…
The Landau Free Energy determines the landscape of order parameter fluctuations that occur in a physical system at thermal equilibrium and, in particular, characterizes the critical phenomena. We propose a semi-analytical approach based on…
Free energy functionals of Ginzburg-Landau type lie at the heart of a broad class of continuum dynamical models, such as the Cahn-Hilliard and Swift-Hohenberg equations. Despite the wide use of such models, the assumptions embodied in the…
Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
In this PhD thesis, we explore and apply methods inspired by the free energy principle to two important areas in machine learning and neuroscience. The free energy principle is a general mathematical theory of the necessary…
The Landau-Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational…
The energy cost of computation has emerged as a central challenge at the intersection of physics and computer science. Recent advances in statistical physics -- particularly in stochastic thermodynamics -- enable precise characterizations…
Landau theory relates phase transitions to the minimization of the Landau functional (e.g., free energy functional), which is expressed as a power series of the order parameter. It has been shown that the critical behavior of certain…
Landau's theory of phase transitions is adapted to treat independently relaxing regions in complex systems using nanothermodynamics. The order parameter we use governs the thermal fluctuations, not a specific static structure. We find that…
We propose a new Monte Carlo algorithm for the free energy calculation based on configuration space sampling. We implement this algorithm for Ising model. Comparison with the exact free energy shows an excellent agreement. We analyse the…
Recent variational studies have demonstrated that the strongly correlated ground states of the fractional quantum Hall (FQH) effect can be captured using machine learning approaches starting from no prior knowledge of the underlying…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range…
Fluctuation relations allow for the computation of equilibrium properties, like free energy, from an ensemble of non-equilibrium dynamics simulations. Computing them for quantum systems, however, can be difficult, as performing dynamic…
The impact of leading collective electronic fluctuations on a free energy of a prototype 1D model for molecular systems is considered within the recently developed Fluctuating Local Field (FLF) approach. The FLF method is a non-perturbative…
We show how any system with morphological degrees of freedom and locally limited free energy will, under the constraints of the free energy principle, evolve toward a neuromorphic morphology that supports hierarchical computations in which…