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.