Related papers: Heat equation from a deterministic dynamics
We present an approximate and heuristic scheme for the derivation of continuum kinetic equations from microscopic dynamics for stochastic, interacting systems. The method consists of a mean-field type, decoupled approximation of the master…
We show that fundamental thermodynamic relations can be derived from deterministic mechanics for a non-ergodic system. This extend a similar derivation for ergodic systems and suggests that ergodicity should not be considered as a…
We study by means of numerical simulations the model of dissipative particle dynamics with energy conservation for the simple case of thermal conduction. It is shown that the model displays correct equilibrium fluctuations and reproduces…
We consider solutions of the linear heat equation with time-dependent singularities. It is shown that if a singularity is weaker than the order of the fundamental solution of the Laplace equation, then it is removable. We also consider the…
Imposing the Petrov-like boundary condition on the hypersurface at finite cutoff, we derive the hydrodynamic equation on the hypersurface from the bulk Einstein equation with electromagnetic field in the near horizon limit. We first get the…
The generalized Gibbs free energy and enthalpy is derived in the framework of nonextensive thermodynamics by using the so-called physical temperature and the physical pressure. Some thermodynamical relations are studied by considering the…
The one-dimensional problem of the nonlinear heat equation is considered. We assume that the heat flow in the origin of coordinates is the power function of time and the initial temperature is zero. Approximate solutions of the problem are…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
Various sharp pointwise estimates for the gradient of solutions to the heat equation are obtained. The Dirichlet and Neumann conditions are prescribed on the boundary of a half-space. All data belong to the Lebesgue space $L^p$. Derivation…
The concept of thermal energy was only fully formulated in the late 19th and early 20th centuries. The search for the understanding of calorific phenomena was what provided the construction and development of the concept of thermal energy.…
We consider the problem of constructing the size dependence for the thermal physical properties of nano-sized objects, taking specific heat as an example. The base methodology is Hill's nanothermodynamics. Having to abstain from use of the…
The microscopic quantum field theory origins of warm inflation dynamics are reviewed. The warm inflation scenario is first described along with its results, predictions and comparison with the standard cold inflation scenario. The basics of…
Despite its historical importance, a perfect gas enclosed by a pistons and in contact with a thermal reservoirs is a system still largely under study. Its thermodynamic properties are not yet well understood when driven under…
Expressions for the quantum fluctuations of energy density have been derived for the subsystems consisting of hot relativistic gas of particles with spin-$\frac{1}{2}$ and mass $m$. Our expressions for the fluctuation depend on the form of…
We investigate heat transport via a charged flexible chain in the presence of magnetic fields. We focus on the Nernst-like effect, where the average positions of particles deviate in the perpendicular direction to the heat flow. This…
We derive a general formulation of the laws of irreversible thermodynamics in the presence of electromagnetism and gravity. For the handling of macroscopic material media, we use as a guide the field equations and the Noether identities of…
Explaining the influence of strong coupling in the dynamics of open quantum systems is one of the most challenging issues in the rapidly growing field of quantum thermodynamics. By using a particular definition of heat, we develop a new…
We establish conditions ensuring either existence or blow-up of nonnegative solutions for the heat equation generated by the Dirichlet fractional Laplacian perturbed by negative potentials on bounded sets. The elaborated theory is supplied…