Related papers: Heat equation from a deterministic dynamics
Thermodynamic formulas for investigating systems with density and/or temperature dependent particle masses are generally derived from the fundamental derivation equality of thermodynamics. Various problems in the previous treatments are…
We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, $F(t)$, has a nontrivial quartic variation. This process,…
The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to…
We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial…
Three different approaches to derive mutual information via thermodynamics are presented where the temperature-dependent energy is given by: (a) $\beta \mathcal{E} = -\ln[P(X,Y)]$, (b) $\beta \mathcal{E} =-\ln[P(Y|X)]$ or (c) $\beta…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
We report model calculations of the time-dependent internal energy and entropy for a single quasi-free massive quantum particle at a constant temperature. We show that the whole process started from a fully coherent quantum state to…
This paper is devoted to the homogenization of the heat conduction equation, with a homogeneous Dirichlet boundary condition, having a periodically oscillating thermal conductivity and a vanishing volumetric heat capacity. A homogenization…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an…
A sharp double-sided Harnack bound is derived for positive solutions of a fractional order heat equation.
We establish three partial differential equation models describing the thermodynamics of the fluid, by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamics laws. What is more, by…
The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a…
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $\phi$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition…
The reheating process in inflationary universe models is considered as an out-of-equilibrium mixture of two interacting and reacting fluids, and studied within the framework of causal, irreversible thermodynamics. The evolution of the…
Observational evidence in space and astrophysical plasmas with long collisional mean free path suggests that more massive charged particles may be preferentially heated. One possible mechanism for this is the turbulent cascade of energy…
We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of…
The Chapman-Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a…
The present work extends the well-known thermodynamic relation $C=\beta ^{2}< \delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest…
We investigate a simple model corresponding to particles driven in opposite directions and interacting via a repulsive potential. The particles move off-lattice on a periodic strip and are subject to random forces as well. We show that this…
We consider the stochastic heat equation whose solution is observed discretely in space and time. An asymptotic analysis of power variations is presented including the proof of a central limit theorem. It generalizes the theory from…