On the formation/dissolution of equilibrium droplets

We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above the ambient gas density. We identify a dimensionless parameter $\Delta\sim(\delta N)^{(d+1)/d}/V$ and a \textrm{universal} value \Deltac=\Deltac(d), and show that a droplet of the dense phase occurs whenever \Delta>\Deltac, while, for \Delta<\Deltac, the excess is entirely absorbed into the gaseous background. When the droplet first forms, it comprises a non-trivial, \textrm{universal} fraction of excess particles. Similar reasoning applies to generic two-phase systems at phase coexistence including solid/gas--where the ``droplet'' is crystalline--and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.Comment: An announcement of a forthcoming rigorous work on the 2D Ising model; to appear in Europhys. Let

How brains make decisions

This chapter, dedicated to the memory of Mino Freund, summarizes the Quantum Decision Theory (QDT) that we have developed in a series of publications since 2008. We formulate a general mathematical scheme of how decisions are taken, using the point of view of psychological and cognitive sciences, without touching physiological aspects. The basic principles of how intelligence acts are discussed. The human brain processes involved in decisions are argued to be principally different from straightforward computer operations. The difference lies in the conscious-subconscious duality of the decision making process and the role of emotions that compete with utility optimization. The most general approach for characterizing the process of decision making, taking into account the conscious-subconscious duality, uses the framework of functional analysis in Hilbert spaces, similarly to that used in the quantum theory of measurements. This does not imply that the brain is a quantum system, but just allows for the simplest and most general extension of classical decision theory. The resulting theory of quantum decision making, based on the rules of quantum measurements, solves all paradoxes of classical decision making, allowing for quantitative predictions that are in excellent agreement with experiments. Finally, we provide a novel application by comparing the predictions of QDT with experiments on the prisoner dilemma game. The developed theory can serve as a guide for creating artificial intelligence acting by quantum rules.Comment: Latex file, 20 pages, 3 figure

Mean-field model of the ferromagnetic ordering in the superconducting phase of ErNi_2B_2C

A mean-field model explaining most of the details in the magnetic phase diagram of ErNi_2B_2C is presented. The low-temperature magnetic properties are found to be dominated by the appearance of long-period commensurate structures. The stable structure at low temperatures and zero field is found to have a period of 40 layers along the a direction, and upon cooling it undergoes a first-order transition at T_C = 2.3 K to a different 40-layered structure having a net ferromagnetic component of about 0.4 mu_B/Er. The neutron-diffraction patterns predicted by the two 40-layered structures, above and below T_C, are in agreement with the observations of Choi et al.Comment: 4 pages, 3 figures (Revtex4

Hidden symmetries for thermodynamics and emergence of relativity

Erik Verlinde recently proposed an idea about the thermodynamic origin of gravity. Though this is a beautiful idea which may resolve many long standing problems in the theories of gravity, it also raises many other problems. In this article I will comment on some of the problems of Verlinde's proposal with special emphasis on the thermodynamical origin of the principle of relativity. It is found that there is a large group of hidden symmetries of thermodynamics which contains the Poincare group of the spacetime for which space is emergent. This explains the thermodynamic origin of the principle of relativity.Comment: V1: 4 pages, comments/criticisms welcomed; V2: references added; V3: typos and minor corrections? V4? substantial changes in Section 3 and other parts mad

On the entropy production of time series with unidirectional linearity

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are only uncorrelated but not statistically independent of the future. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry. For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we show that such a link also exists for the above unidirectional linearity. We study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited to the forward-time conditional probabilities, but not to the backward-time conditionals. The reason for this asymmetry between past and future is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependencies afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward conditionals to the minimal amount of entropy generation.Comment: 16 page

Capillary pressure of van der Waals liquid nanodrops

The dependence of the surface tension on a nanodrop radius is important for the new-phase formation process. It is demonstrated that the famous Tolman formula is not unique and the size-dependence of the surface tension can distinct for different systems. The analysis is based on a relationship between the surface tension and disjoining pressure in nanodrops. It is shown that the van der Waals interactions do not affect the new-phase formation thermodynamics since the effect of the disjoining pressure and size-dependent component of the surface tension cancel each other.Comment: The paper is dedicated to the 80th anniversary of A.I. Rusano

An epitaxial model for heterogeneous nucleation on potent substrates

© The Minerals, Metals & Materials Society and ASM International 2012In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (ΔT ). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h ), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h and ΔT ; h decreases; and ΔT increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.EPSRC Centre for Innovative Manufacturing in Liquid Metal Engineerin

Phase transitions in geometrothermodynamics

Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic metrics for the equilibrium manifold whose curvature becomes singular at those points where phase transitions of first and second order occur. We conclude that the thermodynamic curvature of the equilibrium manifold, as defined in geometrothermodynamics, can be used as a measure of thermodynamic interaction in diverse systems with two and three thermodynamic degrees of freedom

The EPR experiment in the energy-based stochastic reduction framework

We consider the EPR experiment in the energy-based stochastic reduction framework. A gedanken set up is constructed to model the interaction of the particles with the measurement devices. The evolution of particles' density matrix is analytically derived. We compute the dependence of the disentanglement rate on the parameters of the model, and study the dependence of the outcome probabilities on the noise trajectories. Finally, we argue that these trajectories can be regarded as non-local hidden variables.Comment: 11 pages, 5 figure

A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure