A. Pérez-Madrid

Brownian motion in the presence of a temperature gradient

By considering an ensemble of Brownian particles suspended in a heat bath as a thermodynamic system with an internal degree of freedom it is possible to obtain the Fokker-Planck equation for Brownian motion in a temperature gradient, by applying the scheme of non-equilibrium thermodynamics. We recover explicitely the equations derived in particular by Zubarev and Bashkirov using statistical mechanical and kinetic methods. In addition when the temperature gradient does not have an externally imposed magnitude we obtain the differential equation for the temperature field, which is coupled to the Fokker-Planck equation.

Fluctuating hydrodynamics approach to chemical reactions

We have used the thermodynamical description of a chemical reaction as a diffusion process along an internal coordinate to analyze fluctuations in the density of the constituents, which are treated under the framework of fluctuating hydrodynamics. We then obtain a Langevin equation for the density, as a function of the internal coordinate, whose stochastic source statisfies a fluctuation-dissipation theorem. After contraction of the description, by means of integration in the internal coordinate, we derive the Langevin equation for the concentration of reactants and products as well as the statistical properties of the random source which agree with the corresponding results obtained by means of Keizers theory. Application of the formalism is illustrated by considering particular cases. An extension to coupled chemical reactions is also discussed.

Heat transfer between nanoparticles: Thermal conductance for near-field interactions

We analyze the heat transfer between two nanoparticles separated by a distance lying in the near-field domain in which energy interchange is due to the Coulomb interactions. The thermal conductance is computed by assuming that the particles have charge distributions characterized by fluctuating multipole moments in equilibrium with heat baths at two different temperatures. This quantity follows from the fluctuation-dissipation theorem for the fluctuations of the multipolar moments. We compare the behavior of the conductance as a function of the distance between the particles with the result obtained by means of molecular dynamics simulations. The formalism proposed enables us to provide a comprehensive explanation of the marked growth of the conductance when decreasing the distance between the nanoparticles.

Kramers-type picture for crystal nucleation

We introduce a new scheme to analyze the kinetics of homogeneous nucleation in terms of a global order parameter. Our approach is based on the application of the internal degrees of freedom formalism to derive a kinetic equation of the Kramers type formulated for a global reaction coordinate. We provide explicit expressions for the quantities and coefficients involved in the process, suitable for simulation. In addition, our picture recovers in the quasistationary case the transition rate obtained from the method of reactive flux. The equation we present may provide a link between theoretical approaches to homogeneous nucleation (generally formulated in terms of a kinetic equation of the Fokker–Planck type) and simulations (which mostly employ linear response theory). In this context, our scheme provides a theoretical framework to interpret and extend the results obtained in recent simulations.

Origin of the violation of the fluctuation–dissipation theorem in systems with activated dynamics

We analyze the validity of the fluctuation–dissipation theorem for slow relaxation systems in the context of mesoscopic nonequilibrium thermodynamics. We demonstrate that the violation arises as a natural consequence of the elimination of fast variables in the description of a glassy system, and it is intrinsically related to the underlying activated nature of slow relaxation. In addition, we show that the concept of effective temperature, introduced to characterize the magnitude of the violation, is not robust since it is observable-dependent, can diverge, or even be negative.

Stochastic resonance in a system of ferromagnetic particles.

We show that a dispersion of monodomain ferromagnetic particles in a solid phase exhibits stochastic resonance when a driven linearly polarized magnetic field is applied. By using an adiabatic approach, we calculate the power spectrum, the distribution of residence times and the mean first passage time. The behavior of these quantities is similar to their corresponding ones in other systems in which stochastic resonance has also been observed.

INERTIAL EFFECTS IN NON-EQUILIBRIUM THERMODYNAMICS

We discuss inertial effects in systems outside equilibrium within the framework of non-equilibrium thermodynamics. By introducing a Gibbs equation in which the entropy depends on the probability density, we are able to describe a system of Brownian particles immersed in a heat bath in both inertial and diffusion regimes. In the former, a relaxation equation for the diffusion current is obtained whereas in the latter we recover Ficks law. Our approach, which uses the elements of the theory of internal degrees of freedom, constitutes the mesoscopic version of a previous analysis which takes into account the kinetic energy of diffusion.

Fokker–Planck equations for nucleation processes revisited

We present a new approach to analyze homogeneous nucleation based on non-equilibrium thermodynamics. The starting point is the formulation of a Gibbs equation for the variations of the entropy of the system, whose state is characterized by an internal coordinate or degree of freedom. By applying the method of non-equilibrium thermodynamics we then obtain the entropy production corresponding to a diffusion process in the internal space. The linear laws together with the continuity equation lead to a kinetic equation of the Fokker–Planck type.By choosing properly the degree of freedom we are able to obtain a new kinetic equation for a global crystallization order parameter (used in recent simulations), and also we recover some of the existing equations. The consistency of the scheme we propose is proved in the quasi-stationary case. Finally, we also outline the way in which our formalism could be extended to more general situations.

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 non-equilibrium 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.

Heat exchange between two interacting nanoparticles beyond the fluctuation-dissipation regime.

We show that the observed nonmonotonic behavior of the thermal conductance between two nanoparticles when they are brought into contact is originated by an intricate phase space dynamics. Here it is assumed that this dynamics results from the thermally activated jumping through a rough energy landscape. A hierarchy of relaxation times plays the key role in the description of this complex phase space behavior. Our theory enables us to analyze the heat transfer just before and at the moment of contact.