Related papers: Heat equation from a deterministic dynamics
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the…
The energetics of the stochastic process has shown the balance of energy on the mesoscopic level. The heat and the energy defined there are, however, generally different from their macroscopic counterpart. We show that this discrepancy can…
We obtain macroscopic isothermal thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics in contact with a heat bath. The microscopic dynamics is given by a chain of anharmonic oscillators subject to a…
Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…
In this paper we consider the problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional heat equation in the case of nonlocal boundary and integral overdetermination…
In the standard form of the relativistic heat equation used in astrophysics, information propagates instantaneously, rather than being limited by the speed of light as demanded by relativity. We show how this equation nonetheless follows…
We obtain macroscopic adiabatic thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics subject to random collisions with the environment. The microscopic dynamics is given by a chain of oscillators…
Ginzburg-Landau energy models arise as autonomous sto-chastic dynamics for the energies in coupled systems after a weak coupling limit (cf. [3, 6]). We prove here that, under certain conditions, the energy fluctuations of these stochastic…
We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve…
In this paper, we establish the well-posedness of stochastic heat equations on moving domains, which amounts to a study of infinite dimensional interacting systems. The main difficulty is to deal with the problems caused by the time-varying…
This paper consider the mesoscopic limit of a stochastic energy exchange model that is numerically derived from deterministic dynamics. The law of large numbers and the central limit theorems are proved. We show that the limit of the…
We show how the macroscopic state variables pressure, entropy and temperature of equilibrium thermodynamics can be consistently derived from the (quantum) chaotic spectral structure of one or two particles in two-dimensional domains. This…
In this paper, we study fractional order heat equation in higher space-time dimensions and offer specific role of heat flows in various fractional dimensions. We offer fractional solutions of the heat equations thus obtained, and examine…
A methodology is proposed for formulating dynamic equations in thermo-piezoelectric and dissipative media from the first principle of energy conservation. The results are in agreement with those from Hamiltonian principle. Our formulations…
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…
We derive a microscopic expression for the instantaneous diagonal elements of the density matrix $\rho_{nn}(t)$ in the adiabatic basis for an arbitrary time dependent process in a closed Hamiltonian system. If the initial density matrix is…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.
We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first…
Heat and energy are conceptually different, but often are assumed to be the same without justification. An effective method for investigating diffusion properties in equilibrium systems is discussed. With this method, we demonstrate that…