The Metastable Mpemba Effect Corresponds to a Non-monotonic Temperature Dependence of Extractable Work

The Mpemba effect refers to systems whose thermal relaxation time is a non-monotonic function of the initial temperature. Thus, a system that is initially hot cools to a bath temperature more quickly than the same system, initially warm. In the special case where the system dynamics can be described by a double-well potential with metastable and stable states, dynamics occurs in two stages: a fast relaxation to local equilibrium followed by a slow equilibration of populations in each coarse-grained state. We have recently observed the Mpemba effect experimentally in such a setting, for a colloidal particle immersed in water. Here, we show that this metastable Mpemba effect arises from a non-monotonic temperature dependence of the maximum amount of work that can be extracted from the local-equilibrium state at the end of Stage 1.

Thermodynamic aspects of describing the contribution of spontaneous magnetism of electrons to the Hall resistance

On the base of the analysis of quantum-statistical description of the magnetization of electron system containing the spontaneous spin polarization contribution there were found the magnetization and conduction current densities in equilibrium state. It has been shown that equilibrium surface conduction current ensures realization of demagnetization effects but in local equilibrium state determines local equilibrium part of the Hall conductivity. As a result one is given the justification of influence of the spontaneous magnetization on galvanomagnetic effects, which is not related to spin-orbital interaction.

Clausius' entropy revisited

Conventional nonequilibrium thermodynamics is mainly concerned with systems in local equilibrium and their entropy production, due to the irreversible processes which take place in these systems. In this paper, fluids will be considered in a state of local equilibrium. We argue that the main feature of such systems is not the entropy production, but the organization of the flowing currents in such systems. These currents do not only have entropy production, but must also have an organization needed to flow in a certain direction. It is the latter, which is the source of the equilibrium entropy, when the fluid goes from a local equilibrium state to an equilibrium state. This implies a transmutation of the local equilibrium currents' organization into the equilibrium entropy. Alternatively, when a fluid goes from an equilibrium state to a local equilibrium state, its entropy transmutes into the organization of the currents of that state.

Numerical Simulations of Dense Collisional Systems with Extended Distribution of Particle Sizes

The dynamical evolution of dense planetary rings, such as Saturn's rings, is mainly governed by the mutual impacts between macroscopic icy particles. The local equilibrium state is determined by the energy loss in partially inelastic impacts and the viscous gain of energy from the systematic velocity field. Due to frequent impacts the time-scale for the establishment of local energy equilibrium is very short, as compared to the time-scale for radial evolution, which is determined by viscous spreading, and in some cases also by the angular momentum exchange with external satellites. Therefore, local and radial behaviour can, to a large extent be studied separately. This fact is utilized by the local simulation method (Wisdom and Tremaine, 1988; Salo, 1991), following the orbital evolution in a small co-moving region inside the rings with periodic boundary conditions. Compared to previous simulation methods (Salo, 1987) this enables much higher surface density. With the presently attainable number of particles (up to several thousands), realistic modeling of dense regions is possible, taking simultaneously into account the particle size distribution, rotation of particles, as well as vertical self-gravity. By combining several local simulations with different surface densities, it is possible to deduce the expected radial behaviour as well.