2,281 research outputs found
Gibbs Entropy and Irreversibility
This contribution is dedicated to dilucidating the role of the Gibbs entropy
in the discussion of the emergence of irreversibility in the macroscopic world
from the microscopic level. By using an extension of the Onsager theory to the
phase space we obtain a generalization of the Liouville equation describing the
evolution of the distribution vector in the form of a master equation. This
formalism leads in a natural way to the breaking of the BBGKY hierarchy. As a
particular case we derive the Boltzmann equation
Quantum Theory of Irreversibility
A generalization of the Gibbs-von Neumann relative entropy is proposed based
on the quantum BBGKY [Bogolyubov-Born-Green-Kirkwood-Yvon] hierarchy as the
nonequilibrium entropy for an N-body system. By using a generalization of the
Liouville-von Neumann equation describing the evolution of a density super-
operator, it is demonstrated that the entropy production for an isolated system
is non-negative, which provides an arrow of time. Moreover, following the
procedure of non-equilibrium thermodynamics a master matrix is introduced for
which a mi- croscopic expression is obtained. Then, the quantum Boltzmann
equation is derived in terms of a transition superoperator related to that
master matrix
The non-equilibrium work relation. Thermodynamic analysis and microscopic foundations
We discuss the conditions for which the non-equilibrium work relation is
valid by means of thermodynamic and microscopic arguments.Comment: 16 pages 1 figur
Statistical Mechanical Theory of a Closed Oscillating Universe
Based on Newton's laws reformulated in the Hamiltonian dynamics combined with
statistical mechanics, we formulate a statistical mechanical theory supporting
the hypothesis of a closed oscillating universe. We find that the behaviour of
the universe as a whole can be represented by a free entropic oscillator whose
lifespan is nonhomogeneous, thus implying that time is shorter or longer
according to the state of the universe itself given through its entropy. We
conclude that time reduces to the entropy production of the universe and that a
nonzero entropy production means that local fluctuations could exist giving
rise to the appearance of masses and to the curvature of the space
Mesoscopic non-equilibrium thermodynamics approach to the dynamics of polymers
We present a general formalism able to derive the kinetic equations of
polymer dynamics. It is based on the application of nonequilibrium
thermodynamics to analyze the irreversible processes taking place in the
conformational space of the macromolecules. The Smoluchowski equation results
from the analysis of the underlying diffusion process in that space within the
scheme of nonequilibrium thermodynamics. We apply the method to different
situations, concerning flexible, semiflexible and rod-like polymers and to the
case of more concentrated solutions in which interactions become important.Comment: 13 pages (RevTex). To be published in Physica
A Mesoscopic Approach to the ``Negative'' Viscosity Effect in Ferrofluids
We present a mesoscopic approach to analyze the dynamics of a single magnetic
dipole under the influence of an oscillating magnetic field, based on the
formulation of a Fokker-Planck equation. The dissipated power and the viscosity
of a suspension of such magnetic dipoles are calculated from non-equilibrium
thermodynamics of magnetized systems. By means of this method we have found a
non-monotonous behaviour of the viscosity as a function of the frequency of the
field which has been referred to as the ``negative'' viscosity effect.
Moreover, we have shown that the viscosity depends on the vorticity field thus
exhibiting non-Newtonian behaviour. Our analysis is complemented with numerical
simulations which reproduce the behaviour of the viscosity we have found and
extend the scope of our analytical approach to higher values of the magnetic
field.Comment: 9 pages, 2 eps figures, simulations have been adde
Controlling anomalous stresses in soft field-responsive systems
We report a new phenomenon occurring in field-responsive suspensions:
shear-induced anomalous stresses. Competition between a rotating field and a
shear flow originates a multiplicity of anomalous stress behaviors in
suspensions of bounded dimers constituted by induced dipoles. The great variety
of stress regimes includes non-monotonous behaviors, multi-resonances, negative
viscosity effect and blockades. The reversibility of the transitions between
the different regimes and the self-similarity of the stresses make this
phenomenon controllable and therefore applicable to modify macroscopic
properties of soft condensed matter phasesComment: 5 pages, 6 figures, submitted to PR
Stochastic Resonance in Nonpotential Systems
We propose a method to analytically show the possibility for the appearance
of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our
results to the FitzHugh-Nagumo model under a periodic external forcing, showing
that the model exhibits stochastic resonance. The procedure that we follow is
based on the reduction to a one-dimensional dynamics in the adiabatic limit,
and in the topology of the phase space of the systems under study. Its
application to other nonpotential systems is also discussed.Comment: Submitted to Phys. Rev.
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