Onsager-Machlup Theory and Work Fluctuation Theorem for a Harmonically Driven Brownian Particle

We extend Tooru-Cohen analysis for nonequilibrium steady state (NSS) of a Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian particle by considering time dependent external drive protocol. We consider an unbounded charged Brownian particle in the presence of oscillating electric field and prove work fluctuation theorem, which is valid for any initial distribution and at all times. For harmonically bounded and constantly dragged Brownian particle considered by Tooru and Cohen, work fluctuation theorem is valid for any initial condition (also NSS), but only in large time limit. We use Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work distribution function, and describe entropy production rate and properties of dissipation functions for the present system using Onsager-Machlup functional.     

Entropy production and time asymmetry in nonequilibrium fluctuations

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems: namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant.     

Disordered Markovian Brownian ratchets

A model of a Brownian ratchet coupled to a heat bath and driven by a nonequilibrium Poisson white noise is discussed. The formula describing a generated current in terms of the statistical properties of a possible irregular or random potential is derived within the small nonequilibrium noise approximation and illustrated by a few concrete examples. The perturbation technique for Hilbert space operators is used as a mathematical tool.     

Simultaneous Brownian motion of N particles in a temperature gradient

A system of N Brownian particles suspended in a nonuniform heat bath is treated as a thermodynamic system with internal degrees of freedom, in this case their velocities and coordinates. Applying the scheme of nonequilibrium thermodynamics, one then easily obtains the Fokker-Planck equation for simultaneous Brownian motion of N particles in a temperature gradient. This equation accounts for couplings in the motion as a result of hydrodynamic interactions between particles.     

Dynamics of the solid and liquid phases in dilute sheared Brownian suspensions: irreversibility and particle migration

Magnetic resonance measurements of migration and irreversible dynamics in the capillary shear flow of a Brownian suspension are presented. The results demonstrate the presence of phenomena typically associated with concentrated noncolloidal systems and indicate the role of many body hydrodynamics in dilute Brownian suspension transport. The application of concepts from chaos theory and nonequilibrium statistical mechanics is demonstrated.     

Hydrodynamic and brownian fluctuations in sedimenting suspensions

We use a mesoscopic computer simulation method to study the interplay between hydrodynamic and Brownian fluctuations during steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.1-15. Even when the hydrodynamic interactions are an order of magnitude weaker than Brownian forces, they still induce backflow effects that dominate the reduction of the average sedimentation velocity with increasing particle packing fraction. Velocity fluctuations, on the other hand, begin to show nonequilibrium hydrodynamic character for Pe>1.     

Algorithmic complexity of thermal ratchet motion

Thermal ratchets are Brownian models where time-correlated fluctuations coming from a nonequilibrium bath interacting with a spatial asymmetry are sufficient conditions to give rise to transport. The nonequilibrium bath acts as a source of negentropy (physical information). In order to quantitate the transfer of information that occurs in thermal ratchet motion, the Kolmogorov information entropy or algorithmic complexity is investigated. The complexity is measured in terms of the average number of bits per time unit necessary to specify the sequence generated by the system.     

Melting of polydisperse colloidal crystals in nonequilibrium

The influence of a time-dependent oscillatory external field on the melting transition of a polydisperse colloidal crystal is examined by theory and computer simulation. In a monodisperse crystal the field just induces an overall dynamical mode which does not affect the melting line. For a polydisperse sample, on the other hand, the field shifts the melting line towards smaller temperatures. Combining a solid cell approach and a Lindemann criterion in nonequilibrium, a simple theory is presented showing that the temperature shift scales with the square of the relative polydispersity. The theory is in reasonable agreement with nonequilibrium Brownian dynamics computer simulations.     

Depletion forces in nonequilibrium

The concept of effective depletion forces between two fixed big colloidal particles in a bath of small particles is generalized to a nonequilibrium situation where the bath of small Brownian particles is flowing around the big particles with a prescribed velocity. In striking contrast to the equilibrium case, the nonequilibrium forces violate Newton's third law; they are nonconservative and strongly anisotropic, featuring both strong attractive and repulsive domains.     

Slow dynamics of self-diffusion in metastable colloidal fluids

A simple theory for nonequilibrium density fluctuations in concentrated hard-sphere suspensions of interacting Brownian particles with both hydrodynamic and direct interactions is proposed. The correlation effects due to the many-body hydrodynamic interactions among particles are shown to cause a structural arrest in the relaxation of nonequilibrium density fluctuations. A volume fraction dependence of slow relaxation process in concentrated colloidal suspensions is thus explored from a new unifying point of view.     

Noise-Induced Phase Transition: Zero-Dimensional Brownian Particles Varying between Ergodicity and Nonergodicity

We study in phase space a zero-dimensional system of Brownian particles which move in a periodic potential and subject to an internal time derivative Ornstein-Uhlenbeck noise. To resolve the Fokker-Planck equation in such a case, we propose an approximate analytical method. The theoretical predictions exhibit a second order noise-induced nonequilibrium phase transition, which is confirmed by numerical simulation results. The phase transition brings the system from an ergodicity to a nonergodicity phase as the potential barrier height decreases.     

Performance characteristics of Brownian motors

Brownian motors are nonequilibrium systems that rectify thermal fluctuations to achieve directed motion, using spatial or temporal asymmetry. We provide a tutorial introduction to this basic concept using the well-known example of a flashing ratchet, discussing the micro- to nanoscopic scale on which such motors can operate. Because of the crucial role of thermal noise, the characterization of the performance of Brownian motors must include their fluctuations, and we review suitable performance measures for motor coherency and efficiency. Specifically, we highlight that it is possible to determine the energy efficiency of Brownian motors by measuring their velocity fluctuations, without detailed knowledge of the motor function and its energy input. Finally, we exemplify these concepts using a model for an artificial single-molecule motor with internal degrees of freedom.     

Heat fluctuations in a nonequilibrium bath

We measure the energy fluctuations of a Brownian particle confined by an optical trap in an aging gelatin after a very fast quench (less than 1 ms). The strong nonequilibrium fluctuations due to the assemblage of the gel are interpreted, within the framework of fluctuation theorem, as a heat flux from the particle towards the bath. We derive an analytical expression of the heat probability distribution, which fits the experimental data and satisfies a fluctuation relation similar to that of a system in contact with two baths at different temperatures.     

On elimination of fast variables: Applications to nonequilibrium systems

A method developed earliier in the context of Brownian motion for elimination of fast variables is applied to certain proto-type models for nonequilibrium systems. This method is compared with that of Mori et al.     

Entropy production of Brownian macromolecules with inertia

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system can have a negative entropy production rate, and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external force, which includes the transverse Lorentz force, leading to equilibrium.     

Oscillations and fluctuations in a dissipative spin system

A dissipative spin system, which is also considered to be a model for optical fluorescence, is investigated from the viewpoint of Brownian motion of spins. The most probable path and the fluctuations are determined by the quantum mechanical version of the system size expansion method. For the most probable path, the flow lines as well as the time evolutions are obtained exactly. This system exhibits a sort of nonequilibrium phase transition as the strength of an external field exceeds the dissipation. The fluctuations show unusual behaviour associated with the Volterra-like oscillations above threshold.     

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski-reactive like equation; for the particle’s momentum density, a generalized Ohm’s-like equation; and for the particle’s energy density, a Maxwell-Cattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann’s entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles.