Related papers: Constructive Cavity Method
The analytical gradient for periodic systems is presented, for the case of metallic systems. The total energy and the free energy are computed on the Hartree-Fock or density functional level, with the wave function being expanded in terms…
Recently, we clarify connection of spatial constraint and equilibrium macroscopic properties in disordered states of classical system under the fixed composition; namely few special microscopic states, independent of constituent elements,…
Within this work we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable to systems across…
Work extractable from quantum system can be viewed as a resource to perform some tasks. Here, we try to related the work extractable to some resource theory. To do this, we consider completely passive states and passive states as free…
We obtain expressions for the Casimir energy and force following an approach which may be applied to cavities made up of arbitrary materials. In the case of planar cavities we obtain the well known Lifshitz formula. The approach is easily…
We show that our procedure of constructing excited-state energy functionals by splitting k-space, employed so far to obtain exchange energies of excited-states, is quite general. We do so by applying the same method to construct modified…
In this short note, we prove a central limit theorem for the free energy in the Ghatak- Sherrington model at high enough temperatures, based on a generalization of the stochastic calculus method for the SK model derived in [CN95, Tin05].
In a large variety of quantum mechanical systems, we show that the full non-perturbative expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from…
In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
The imaginary-time path integral representation of the canonical partition function of a quantum system and non-equilibrium work fluctuation relations are combined to yield methods for computing free energy differences in quantum systems…
The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with…
We present, for the Ising model on the Cayley tree, some explicit formulae of the free energies (and entropies) according to boundary conditions (b.c.). They include translation-invariant, periodic, Dobrushin-like b.c., as well as those…
The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory…
We prove a number of results concerning the large $N$ asymptotics of the free energy of a random matrix model with a polynomial potential $V(z)$. Our approach is based on a deformation $\tau_tV(z)$ of $V(z)$ to $z^2$, $0\le t<\infty$ and on…
In this paper we demonstrate how chemical free energy can be produced by a geological process. We provide a thermodynamic framework in which to assess how life emerged at the off-axis hydrothermal vent system; the RNA - clays system has…
We consider a random Hamiltonian $H:\Sigma\to\mathbb R$ defined on a compact space $\Sigma$ that admits a transitive action by a compact group $\mathcal G$. When the law of $H$ is $\mathcal G$-invariant, we show its expected free energy…
We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice $\Z^d$. Our method is based on representing the free energy and surface pressure in terms of…
We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side…
Free energy is arguably the most importance function(al) for understanding of molecular systems. A number of rigorous and approximate free energy calculation/estimation methods have been developed over many decades. One important issue, the…