1,612 research outputs found
Generalized Phase Rules
For a multi-component system, general formulas are derived for the dimension
of a coexisting region in the phase diagram in various state spaces.Comment: In the revised manuscript, physical meanings of D's are explained by
adding three figures. 10 pages, 3 figure
Equilibrium and nonequilibrium thermodynamics of particle-stabilized thin liquid films
Our recent quasi-two-dimensional thermodynamic description of thin-liquid
films stabilized by colloidal particles is generalized to describe nonuniform
equilibrium states of films in external potentials and nonequilibrium transport
processes produced in the film by gradients of thermodynamic forces. Using a
Monte--Carlo simulation method, we have determined equilibrium equations of
state for a film stabilized by a suspension of hard spheres. Employing a
multipolar-expansion method combined with a flow-reflection technique, we have
also evaluated the short-time film-viscosity coefficients and collective
particle mobility.Comment: 16 pages, 10 figure
Macroscopic entanglement of many-magnon states
We study macroscopic entanglement of various pure states of a one-dimensional
N-spin system with N>>1. Here, a quantum state is said to be macroscopically
entangled if it is a superposition of macroscopically distinct states. To judge
whether such superposition is hidden in a general state, we use an essentially
unique index p: A pure state is macroscopically entangled if p=2, whereas it
may be entangled but not macroscopically if p<2. This index is directly related
to the stability of the state. We calculate the index p for various states in
which magnons are excited with various densities and wavenumbers. We find
macroscopically entangled states (p=2) as well as states with p=1. The former
states are unstable in the sense that they are unstable against some local
measurements. On the other hand, the latter states are stable in the senses
that they are stable against local measurements and that their decoherence
rates never exceed O(N) in any weak classical noises. For comparison, we also
calculate the von Neumann entropy S(N) of a subsystem composed of N/2 spins as
a measure of bipartite entanglement. We find that S(N) of some states with p=1
is of the same order of magnitude as the maximum value N/2. On the other hand,
S(N) of the macroscopically entangled states with p=2 is as small as O(log N)<<
N/2. Therefore, larger S(N) does not mean more instability. We also point out
that these results are analogous to those for interacting many bosons.
Furthermore, the origin of the huge entanglement, as measured either by p or
S(N), is discussed to be due to the spatial propagation of magnons.Comment: 30 pages, 5 figures. The manuscript has been shortened and typos have
been fixed. Data points of figures have been made larger in order to make
them clearly visibl
AFM pulling and the folding of donor-acceptor oligorotaxanes: phenomenology and interpretation
The thermodynamic driving force in the self-assembly of the secondary
structure of a class of donor-acceptor oligorotaxanes is elucidated by means of
molecular dynamics simulations of equilibrium isometric single-molecule force
spectroscopy AFM experiments. The oligorotaxanes consist of
cyclobis(paraquat-\emph{p}-phenylene) rings threaded onto an oligomer of
1,5-dioxynaphthalenes linked by polyethers. The simulations are performed in a
high dielectric medium using MM3 as the force field. The resulting force vs.
extension isotherms show a mechanically unstable region in which the molecule
unfolds and, for selected extensions, blinks in the force measurements between
a high-force and a low-force regime. From the force vs. extension data the
molecular potential of mean force is reconstructed using the weighted histogram
analysis method and decomposed into energetic and entropic contributions. The
simulations indicate that the folding of the oligorotaxanes is energetically
favored but entropically penalized, with the energetic contributions overcoming
the entropy penalty and effectively driving the self-assembly. In addition, an
analogy between the single-molecule folding/unfolding events driven by the AFM
tip and the thermodynamic theory of first-order phase transitions is discussed
and general conditions, on the molecule and the cantilever, for the emergence
of mechanical instabilities and blinks in the force measurements in equilibrium
isometric pulling experiments are presented. In particular, it is shown that
the mechanical stability properties observed during the extension are
intimately related to the fluctuations in the force measurements.Comment: 42 pages, 17 figures, accepted to the Journal of Chemical Physic
Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities
The Partition function of two Hard Spheres in a Hard Wall Pore is studied
appealing to a graph representation. The exact evaluation of the canonical
partition function, and the one-body distribution function, in three different
shaped pores are achieved. The analyzed simple geometries are the cuboidal,
cylindrical and ellipsoidal cavities. Results have been compared with two
previously studied geometries, the spherical pore and the spherical pore with a
hard core. The search of common features in the analytic structure of the
partition functions in terms of their length parameters and their volumes,
surface area, edges length and curvatures is addressed too. A general framework
for the exact thermodynamic analysis of systems with few and many particles in
terms of a set of thermodynamic measures is discussed. We found that an exact
thermodynamic description is feasible based in the adoption of an adequate set
of measures and the search of the free energy dependence on the adopted measure
set. A relation similar to the Laplace equation for the fluid-vapor interface
is obtained which express the equilibrium between magnitudes that in extended
systems are intensive variables. This exact description is applied to study the
thermodynamic behavior of the two Hard Spheres in a Hard Wall Pore for the
analyzed different geometries. We obtain analytically the external work, the
pressure on the wall, the pressure in the homogeneous zone, the wall-fluid
surface tension, the line tension and other similar properties
Neutron Fermi Liquids under the presence of a strong magnetic field with effective nuclear forces
Landau's Fermi Liquid parameters are calculated for non-superfluid pure
neutron matter in the presence of a strong magnetic field at zero temperature.
The particle-hole interactions in the system, where a net magnetization may be
present, are characterized by these parameters in the framework of a multipolar
formalism. We use either zero- or finite-range effective nuclear forces to
describe the nuclear interaction. Using the obtained Fermi Liquid parameters,
the effect of a strong magnetic field on some bulk magnitudes such as
isothermal compressibility and spin susceptibility is also investigated.Comment: 20 pages, 10 figure
Geometric description of BTZ black holes thermodynamics
We study the properties of the space of thermodynamic equilibrium states of
the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole in (2+1)-gravity. We use the
formalism of geometrothermodynamics to introduce in the space of equilibrium
states a dimensional thermodynamic metric whose curvature is non-vanishing,
indicating the presence of thermodynamic interaction, and free of
singularities, indicating the absence of phase transitions. Similar results are
obtained for generalizations of the BTZ black hole which include a Chern-Simons
term and a dilatonic field. Small logarithmic corrections of the entropy turn
out to be represented by small corrections of the thermodynamic curvature,
reinforcing the idea that thermodynamic curvature is a measure of thermodynamic
interaction
Bead, Hoop, and Spring as a Classical Spontaneous Symmetry Breaking Problem
We describe a simple mechanical system that involves Spontaneous Symmetry
Breaking. The system consists of two beads constrained to slide along a hoop
and attached each other through a spring. When the hoop rotates about a fixed
axis, the spring-beads system will change its equilibrium position as a
function of the angular velocity. The system shows two different regions of
symmetry separated by a critical point analogous to a second order transition.
The competitive balance between the rotational diynamics and the interaction of
the spring causes an Spontaneous Symmetry Breaking just as the balance between
temperature and the spin interaction causes a transition in a ferromagnetic
system. In addition, the gravitational potential act as an external force that
causes explicit symmetry breaking and a feature of first-order transition. Near
the transition point, the system exhibits a universal critical behavior where
the changes of the parameter of order is described by the critical exponent
beta =1/2 and the susceptibility by gamma =1. We also found a chaotic behavior
near the critical point. Through a demostrative device we perform some
qualitative observations that describe important features of the system.Comment: 7 pages, 2 tables, 30 figures, LaTeX2
Magnetic properties and critical behavior of disordered Fe_{1-x}Ru_x alloys: a Monte Carlo approach
We study the critical behavior of a quenched random-exchange Ising model with
competing interactions on a bcc lattice. This model was introduced in the study
of the magnetic behavior of Fe_{1-x}Ru_x alloys for ruthenium concentrations
x=0%, x=4%, x=6%, and x=8%. Our study is carried out within a Monte Carlo
approach, with the aid of a re-weighting multiple histogram technique. By means
of a finite-size scaling analysis of several thermodynamic quantities, taking
into account up to the leading irrelevant scaling field term, we find estimates
of the critical exponents \alpha, \beta, \gamma, and \nu, and of the critical
temperatures of the model. Our results for x=0% are in excellent agreement with
those for the three-dimensional pure Ising model in the literature. We also
show that our critical exponent estimates for the disordered cases are
consistent with those reported for the transition line between paramagnetic and
ferromagnetic phases of both randomly dilute and Ising models. We
compare the behavior of the magnetization as a function of temperature with
that obtained by Paduani and Branco (2008), qualitatively confirming the
mean-field result. However, the comparison of the critical temperatures
obtained in this work with experimental measurements suggest that the model
(initially obtained in a mean-field approach) needs to be modified
Effective Free Energy for Individual Dynamics
Physics and economics are two disciplines that share the common challenge of
linking microscopic and macroscopic behaviors. However, while physics is based
on collective dynamics, economics is based on individual choices. This
conceptual difference is one of the main obstacles one has to overcome in order
to characterize analytically economic models. In this paper, we build both on
statistical mechanics and the game theory notion of Potential Function to
introduce a rigorous generalization of the physicist's free energy, which
includes individual dynamics. Our approach paves the way to analytical
treatments of a wide range of socio-economic models and might bring new
insights into them. As first examples, we derive solutions for a congestion
model and a residential segregation model.Comment: 8 pages, 2 figures, presented at the ECCS'10 conferenc
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