We present an overview of some results we have obtained recently (A. Sain, Manu and R. Pandit, Phys. Rev. Lett. 81 (1998) 4377) from a pseudospectral study of the randomly forced Navier–Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance ∼k4−d−y, with k...

A mean-field approach (filtering out subgrid scales) is applied to the Boltzmann equation in order to derive a subgrid turbulence model based on kinetic theory. It is demonstrated that the only Smagorinsky type model which survives in the hydrodynamic limit on the viscosity time scale is the...

We analyze some models of nonequilibrium systems proposed in the past decade which derive the laws of irreversible thermodynamics from deterministic dynamics. We find that these models do not posses the crucial property of local thermodynamic equilibrium, since they represent noninteracting...

Markov chain models on a mesoscopic level are a widely used description for complex systems. They are based on the assumption that certain sets of microstates can be coarse grained as their internal dynamics is faster than the time scales considered in the modeling. Here we analyze...

Theoretical evidence derived from linear irreversible thermodynamics (LIT) jointly with Burnett’s solution of Boltzmann’s gas-kinetic equation is used to show that fluid mechanics and transport processes in both gaseous and liquid continua require the use of two independent velocities rather...

A non-equilibrium statistical theory for aging dissipative systems formed by atoms is developed and applied to electromigration damage in conductors. A modification of Black’s mean failure time is presented. We describe the experimental relationship between the initial rate of increase in the...

In this work we study, at the single molecular level, the thermodynamic and dynamic characteristics of an enzymatic reaction comprising a rate limiting step. We investigate how the stability of the enzyme-state stationary probability distribution, the reaction velocity, and its efficiency of...

A recent theory by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim predicts a temporal asymmetry in the fluctuation–relaxation paths of certain observables of nonequilibrium systems in local thermodynamic equilibrium. We find temporal asymmetries in the fluctuation–relaxation paths of a...

Using the kinetic description of a binary mixture of dissimilar hard spheres following a standard-like Enskog theory, we prove the reciprocity of the Onsager relations within the rigorous framework. This proof, added to previous results, places our description in complete agreement with linear...

In the present work we derive the volume continuity equation and demonstrate its use to define the volume frame of reference in the multicomponent, compressible systems. The volume velocity (material velocity) is a unique frame of reference for all internal forces and processes, e.g., the mass...