Related papers: Heat equation from a deterministic dynamics
We discuss contributions to the thermopower in an electron fluid. A simple argument based on Newton's second law with the pressure gradient as the force suggests that the thermopower is given by a thermodynamic derivative, viz., the entropy…
We derive a condition for the realizability of heat released in nondeterministic processes from a fluctuation theorem, showing that this condition is strictly stronger than the probabilistic form of the second law of thermodynamics. With…
It has been observed in many numerical simulations, experiments and from various theoretical treatments that heat transport in one-dimensional systems of interacting particles cannot be described by the phenomenological Fourier's law. The…
In this work we study in a formal way the density dependent hadron field theory at finite temperature for nuclear matter. The thermodynamical potential and related quantities, as energy density and pressure are derived in two different…
This paper deals with the heat equation posed in a bounded regular domain coupled with a dynamical boundary condition of reactive-diffusive type, involving the Laplace-Beltrami operator. We prove well-posedness of the problem together with…
We derive the dark energy fluid equation of state $P = -\epsilon = {\rm const.}$ as an extremum of entropy, subject to the Hamiltonian constraint of General Relativity. However, we identify perturbations that can render this extremum an…
We consider stationary driven systems in contact with a thermal equilibrium bath. There is a constant (Joule) heat dissipated from the steady system to the environment as long as all parameters are unchanged. As a natural generalization…
We study some mechanical problems in which a friction force is acting on the system. Using the fundamental concepts of state, time evolution and energy conservation we explain how to extend Newtonian mechanics to thermodynamics. We arrive…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
We propose a new formulation of stochastic thermodynamics for systems subjected to nonequilibrium constraints (i.e. broken detailed balance at steady state) and furthermore driven by external time-dependent forces. A splitting of the second…
In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of…
Conversations about weather, environment, health, cuisine, and even politics, all involve the word "temperature". It was an attempt to understand the working of heat engines that gave the temperature a clear definition. In this Note we put…
We investigate heat propagation in rigidly rotating bodies within the theory of general relativity. Using a first-order gradient expansion, we derive a universal partial differential equation governing the temperature evolution. This…
A self-consistent approach based on finite temperature Green's functions is used to investigate thermodynamic properties of nuclear matter. The internal energy is derived from the diagrams associated to the interaction energy. Pressure and…
With the discussion of three examples, we aim at clarifying the concept of energy transfer associated with dissipation in mechanics and in thermodynamics. The dissipation effects due to dissipative forces, such as the friction force between…
We study the non-equilibrium thermodynamics of single Brownian macromolecules immersed in water solvent. They are under both a hydrodynamic interaction and a feedback control on their movement by an external agent. The macromolecules are…
An expression for the internal energy of a fluid element in a weakly coupled, magnetized, anisotropic plasma is derived from first principles. The result is a function of entropy, particle density and magnetic field, and as such plays the…
Thermodynamics of magnetic materials is discussed in practical, lab-oriented terms. In the common experimental configuration in which the external magnetic field comes from a solenoidal coil connected to a power supply, magnetic work is…
The interplay between quantum-mechanical properties, such as coherence, and classical notions, such as energy, is a subtle topic at the forefront of quantum thermodynamics. The traditional Carnot argument limits the conversion of heat to…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…