Related papers: Heat equation from a deterministic dynamics
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…
Let u = {u(t, x), t $\in$ [0, T ], x $\in$ R d } be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with respect…
In Stochastic Thermodynamics, heat is a random variable with a probability distribution associated. Studies of the distribution of heat are mostly in the overdamped regime and in one dimension. Here we solve the heat distribution in the…
A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented.…
This work continues the investigation in two recent papers on the quantum thermodynamics of spacetimes, 1) placing what was studied in [1] for thermal quantum fields in the context of early universe cosmology, and 2) extending the…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
After a discussion on the state of local equilibrium with temperature inhomogeneity, comparing mixture state reprsentation in statistical mechanics and pure state representation in thermo field dynamics, a simple model is solved to show…
How to rigorously define thermodynamic quantities such as heat, work, and internal energy in open quantum systems driven far from equilibrium remains a significant open question in quantum thermodynamics. Heat is a quantity whose…
Originally formulated for macroscopic machines, the laws of thermodynamics were recently shown to hold for quantum systems coupled to ideal sources of work (external classical fields) and heat (systems at equilibrium). Ongoing efforts have…
We present a fluctuation relation for heat dissipation in a nonequilibrium system. A nonequilibrium work is known to obey the fluctuation theorem in any time interval $t$. A heat, which differs from a work by an energy change, is shown to…
The variational heat equation is a nonlinear, parabolic equation not in divergence form that arises as a model for the dynamics of the director field in a nematic liquid crystal. We present a finite difference scheme for a transformed,…
The aim of this paper is to study the $d$-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter $% H\in (0,1)$ in…
We study the heat equation with a random potential term. The potential is a one-sided stable noise, with positive jumps, which does not depend on time. To avoid singularities, we define the equation in terms of a construction similar to the…
In this article, we consider the problem of homogenising the linear heat equation perturbed by a rapidly oscillating random potential. We consider the situation where the space-time scaling of the potential's oscillations is \textit{not}…
We show that it is possible to construct microscopic-level discrete equations from macroscopic modeling PDEs for heat conduction in one space dimension. The significance of this result is that, in general, one starts from microscopic…
Macroscopic thermodynamics of equilibrium is constructed for systems obeying power-law canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is…
We study fragmentation of small atomistic clusters via molecular dynamics. We calculate the time scales related to fragment formation and emission. We also show that some degree of thermalization is achieved during the expansion process,…
Thermal gradients lead to macroscopic fluid motion if a confining surface is present along the gradient. This fundamental nonequilibrium effect, known as thermo-osmosis, is held responsible for particle thermophoresis in colloidal…
The concept of environmental interface is defined and analyzed from the point of view of the possible source of non-standard behaviour. The energy balance equation is written for the interface where all kinds of energy transfer occur. It is…