Related papers: Some interesting observations on the free energy p…
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. As an extension of Welling and Teh (2001), we define the Gaussian fractional Bethe free…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
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,…
We derive a upper bound on the free energy of a Bose gas system at density $\rho$ and temperature $T$. In combination with the lower bound derived previously by Seiringer \cite{RS1}, our result proves that in the low density limit, i.e.,…
We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves effectively as a system of non-interacting…
Energy has no definition, except that given by a conservation principle which essentially amounts to defining it as the elements of an open list of unknown cardinality. Entropy, identified by Shannon as information we lack, has too many…
An expression for the free energy of embryo formation is constructed and analyzed. The Gibbs dividing surfaces method is used to attain a coincidence between Laplace formula for critical embryo and integral definitions of concenterations…
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 finiteness of fossil fuels implies that future electric power systems may predominantly source energy from fuel-free renewable resources like wind and solar. Evidently, these power systems without fuel will be environmentally benign,…
The possibility of the existence of magnetic charges is one of the greatest unsolved issues of the physics of this century. The concept of magnetic monopoles has at least two attractive features: (i) Electric and magnetic fields can be…
We present a detailed analysis of the universal relationship between grain boundary (GB) free energy and GB self-diffusion coefficient derived by Borisov et al. (1964). This relationship was expressed by a simple equation that was used in…
Several aspects of the theory of the coexistence of phases and equilibrium forms are discussed. In section 1, the problem is studied from the point of view of thermodynamics. In section 2, the statistical mechanical theory is introduced. We…
The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While…
A common approach to study nucleation rates is the estimation of free-energy barriers. This usually requires knowledge about the shape of the forming droplet, a task that becomes notoriously difficult in macromolecular setups starting with…
We investigate the transient bubbles that spontaneously appear in a simple liquid using molecular simulations. The objective is to deduce the free-energy of formation of the bubbles $W(s)$ from the bubble size distribution $p(s)$ through…
For time-dependent states generated by an external operation, a generalized free energy may be introduced by the relative entropy with respect to an equilibrium state realized after sufficient relaxation from the time-dependent states.…
The collective phenomena in physics and cooperative phenomena in biology/chemistry is compared in terms of the variational description. The maximum energy dissipation principle is employed and the cost-like functional is chosen according to…
The so-called "free will axiom" is an essential ingredient in many discussions concerning hidden variables in quantum mechanics. In this paper we argue that "free will" can be defined in different ways. The definition usually employed is…
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…
The principles behind the computation of protein-ligand binding free energies by Monte Carlo integration are described in detail. The simulation provides gas-phase binding free energies that can be converted to aqueous energies by solvation…