Statistical mechanics provides a well-established link between microscopic equilibrium states and thermodynamics. If one considers systems out of equilibrium, the link between microscopic dynamical properties and nonequilibrium macroscopic states is more difficult to establish [1,2]. For systems lying near equilibrium, linear response theory provides a route to derive linear macroscopic laws an...

The mathematical physics of mechanical systems in thermal equilibrium is a well studied, and relatively easy, subject, because the Gibbs distribution is in general an adequate guess for the equilibrium state. On the other hand, the mathematical physics of non-equilibrium systems, such as that of a chain of masses connected with springs to two (infinite) heat reservoirs is more difficult, precis...

By designating a system as “near equilibrium”, we mean that the system is perturbed from its equilibrium state by some time-dependent external force f(t). The external force is deterministic, not random; typical examples include mechanical forces and forces due to an applied electric or magnetic field. This force drives the expectation values of some of the system’s observables away from their ...

Local Shannon entropy lies at the heart of modern thermodynamics, with much discussion of trajectory-dependent entropy production. When taken at both boundaries of a process in phase space, it reproduces the second law of thermodynamics over a finite time interval for small scale systems. However, given that entropy is an ensemble property, it has never been clear how one can assign such a quan...

The soil environment immediately around a root frequently has a larger number of microorganisms compared to soil just a few millimeters away from a root. This zone of influence is called the rhizosphere (Rovira, 1991), which is composed of many groups of organisms that are capable of affecting plant health beneficially and deleteriously (Schippers et al., 1987). Putting greens are artificially ...

The occurrence of contaminants in wastewaters, and their behavior during wastewater treatment and production of drinking water are key issues to re-use water resources. The present research aims to remove caffeine from aqueous solutions via adsorption technique, using Multi-Wall Carbon Nanotubes (MWCNTs) as an adsorbent under different experimental conditions. The processing variables such as p...

Introduction Lutein is a carotenoid that can be found in dark green and yellow vegetables, fruits and egg yolk. Lutein, like other carotenoids, is an antioxidant. Sources Lutein and a close chemical zeaxanthin are xanthophyll carotenoids found in a wide variety of plant foods, especially dark green leafy vegetables, such as kale, spinach, turnip greens, and collards. Their concentrations in the...