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Optimality principles in nonequilibrium transport networks are linked to a thermodynamic formalism based on generalized transport potentials endowed with Legendre duality and related contact structure. This allows quantifying the distance…
We consider the governing equations for the motion of compressible fluid on an evolving surface from both energetic and thermodynamic points of view. We employ our energetic variational approaches to derive the momentum equation of our…
In this paper, a new nonlinear heat equation is studied that arises as a model of the collective behavior of automated vehicles. The properties of the solutions of this equation are studied by introducing the appropriate notion of a weak…
Some analogies between different nonequilibrium heat conduction models, particularly, random walk, discrete variable model, and Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that…
According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal compressible two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable,…
This paper is a non-technical, informal presentation of our theory of the second law of thermodynamics as a law that is independent of statistical mechanics and that is derivable solely from certain simple assumptions about adiabatic…
The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy…
The letter considers non-isothermal fluid flows and revises simplifications of basic hydrodynamic equations for such flows arriving eventually to a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of…
In this work, we develop a new compatible finite element formulation of the thermal shallow water equations that conserves energy and mathematical entropies given by buoyancy-related quadratic tracer variances. Our approach relies on…
Thermodynamics allows the application of Statistical Mechanics to finite and even small systems. As surface effects cannot be scaled away, one has to be careful with the standard arguments of splitting a system into two or bringing two…
Thermal conduction is an important energy transfer and damping mechanism in astrophysical flows. Fourier's law - the heat flux is proportional to the negative temperature gradient, leading to temperature diffusion - is a well-known…
Transport properties in gases are significantly affected by temperature. In previous works it has been shown that when the thermal agitation in a gas is high enough, such that relativistic effects become relevant, heat dissipation is driven…
Materials that are constantly driven out of thermodynamic equilibrium, such as active and living systems, typically violate the Einstein relation. This may arise from active contributions to particle fluctuations which are unrelated to the…
The Second Law of Thermodynamics asserts that the physical entropy of an adiabatic system is an increasing function in time. In this paper we will study a more stringent version of this law, according to which the entropy should not only…
Predicting the stable phase configuration in a liquid-gas system becomes a fundamental challenge when the stratification favored by gravity conflicts with arrangements induced by heat flow, particularly because standard equilibrium…
We numerically determine the entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the…
Effects of collective modes on thermoelectric properties of a charge density system is studied. We derive the temperature dependence of thermoelectric power and thermal conductivity by applying the linear response theory to Fr\"ohlich…
In spirit of the principle of least action, which means that when a perturbation is applied to a physical system its reaction is such that it modifies its state to "agree" with the perturbation by "minimal" change of its initial state. In…
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…
People are well aware that, inherently, certain small-scale nonchaotic particle movements are not governed by thermodynamics. Usually, such phenomena are studied by kinetic theory and their energy properties are considered "trivial". In…