Related papers: Modeling of heat conduction through rate equations
We show that heat defines a gauge connection on a line bundle over work configurations. Vanishing curvature is equivalent to the local existence of entropy and temperature functions such that heat can be expressed as $TdS$. A conjecture of…
We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory which includes the usual heat equation subject to a dynamic boundary condition as a special case. We investigate the…
In statistical mechanics the zeroth law of thermodynamics is taken as a postulate which, as its name indicates, logically precedes the first and second laws. Treating it as a postulate has consequences for how temperature is introduced into…
All physical theories should obey the second law of thermodynamics. However, existing proposals to describe the dynamics of hybrid classical-quantum systems either violate the second law or lack a proof of its existence. Here we rectify…
Numerical simulation of steady-state heat conduction is common for thermal engineering. The simulation process usually involves mathematical formulation, numerical discretization and iteration of discretized ordinary or partial differential…
We re-derive the expression for the heat current for a classical system subject to periodic boundary conditions and show that it can be written as a sum of two terms. The first term is a time derivative of the first moment of the system…
We provide a stochastic mathematical representation for Clausius' and Kelvin-Planck's statements of the Second Law of Thermodynamics in terms of the entropy productions of a finite, compact driven Markov system and its lift. A surjective…
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…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…
We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum…
For a thermal conductivity that is spatially uniform and independent of temperature, Fourier's law of heat transfer predicts a curl-free heat-flux. In the quasi-ballistic phonon transport regime, where the Fourier law breaks down, it has…
On the one hand, the dissipated heat of a thermodynamic work extraction process upper bounds the non-predictive information, which the associated system encodes about its environment. Thus, emergent information processing capabilities can…
Thermal conductivities are routinely calculated in molecular dynamics simulations by keeping the boundaries at different temperatures and measuring the slope of the temperature profile in the bulk of the material, explicitly using Fourier's…
Optical, acoustic, hydrodynamic, and thermal defect systems are often studied by analogy with each other. This may indicate that we may find a emergent theory for constitutive relations of classical defect systems. Start with thermal…
The problem of structure formation in relativistic dissipative fluids was analyzed in a previous work within Eckart's framework, in which the heat flux is coupled to the hydrodynamic acceleration, additional to the usual temperature…
Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we…
The general isotropic constitutive equations of heat conduction with second sound and ballistic propagation in isotropic materials is given using Non-Equilibrium Thermodynamics with Internal Variables (NET-IV). The consequences of Onsager…
A simple vibrational model of heat transfer in two-dimensional (2D) fluids relates the heat conductivity coefficient to the longitudinal and transverse sound velocities, specific heat, and the mean interatomic separation. This model is…
In this paper a thermodynamical derivation of the quantum potential is pro- posed. Within the framework of Bohmian mechanics we show how the quantum potential can be derived, by adding an additional informational degree of freedom to the…
Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change,…