471 research outputs found
On the formation/dissolution of equilibrium droplets
We consider liquid-vapor systems in finite volume at parameter
values corresponding to phase coexistence and study droplet formation due to a
fixed excess of particles above the ambient gas density. We identify
a dimensionless parameter 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
Š 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 (ÎT ). 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 ÎT ; h decreases; and ÎT 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
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