Related papers: Thermodynamic hierarchies of evolution equations
The negative integrable hierarchies of shallow water waves and dispersionless Toda lattice equations are considered. The integrability is shown by explicit construction of an infinite set of conservation laws.
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
We consider two statistically independent systems described by the same entropy belonging to the two-parameter family of Sharma-Mittal. Assuming a weak interaction among the systems, allowing in this way an exchange of heat and work, we…
A consistent description of a shear flow, the accompanied viscous heating, and the associated entropy balance is given in the framework of a deterministic dynamical system, where a multibaker dynamics drives two fields: the velocity and the…
Results of heat pulse experiments in various artificial and natural materials are reported in the paper. The experiments are performed at room temperature with macroscopic samples. It is shown that temperature evolution does not follow the…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
We analyse the effects of thermal conduction in a relativistic fluid, just after its departure from hydrostatic equilibrium, on a time scale of the order of thermal relaxation time. It is obtained that the resulting evolution will…
Classical thermodynamics describes physical systems in thermodynamic equilibrium, characterized in particular by the absence of macroscopic motion. Global non-equilibrium thermodynamics extends this framework to include physical systems in…
Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…
Thermodynamics is usually developed starting from entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example in the context of local…
The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of…
It is seen how to write the standard\^E form of the four partial differential equations in four unknowns of anisotropic thermoelasticity as a single equation in one variable, in terms of isothermal and isentropic wave operators. This…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…
An analytical model of unsteady heat transfer in a one-dimensional harmonic crystal is presented. A nonlocal temperature is introduced as a generalization of the kinetic temperature. A closed equation determining unsteady thermal processes…
A heat conduction problem is studied using extended hydrodynamic equations obtained from Enskog's equation for a simple case of two planar systems in contact through a porous wall. One of the systems is in equilibrium and the other one in a…
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with…
We provide a non-equilibrium thermodynamic description of the life-cycle of a droplet based, chemically feasible, system of protocells. By coupling the protocells metabolic kinetics with its thermodynamics, we demonstrate how the system can…
The main objective of this paper is to show that, within the present framework of the kinetic theoretical approach to irreversible thermodynamics, there is no evidence that provides a basis to modify the ordinary Fourier equation relating…
The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local…