Related papers: Dynamical system analysis and thermal evolution of…
It is shown that a recent result regarding the average rate of evolution of a dynamical system at equilibrium in combination with the quantization of geometric areas coming from LQG, implies the validity of Kepler's Second Law of planetary…
We study the radial relaxation dynamics toward equilibrium and time-periodic pulsating spherically symmetric gas bubbles in an incompressible liquid due to thermal effects. The asymptotic model ([A. Prosperetti, J. Fluid Mech., 1991] and…
The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws…
We present an analytic formalism that describes the evolution of the stellar, gas, and metal content of galaxies. It is based on the idea, inspired by hydrodynamic simulations, that galaxies live in a slowly-evolving equilibrium between…
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…
Consider at a finite temperature $T$ a superfluid moving with a velocity $v$ relative to the thermal bath or its normal component. From Landau's argument there exists a critical $v_c (T)$ beyond which excitations can be spontaneously…
The kernel of the evolution equation is used to build a mathematical theory of thermal phenomena of gaseous and condensed matter. The group velocity of sound and the molar density are proposed to be its two thermal variables that replace…
There is a paradox in the standard model of cosmology. How can matter in the early universe have been in thermal equilibrium, indicating maximum entropy, but the initial state also have been low entropy (the "past hypothesis"), so as to…
We investigate the laws of thermodynamics in an accelerating universe driven by dark energy with a time-dependent equation of state. In the case we consider that the physically relevant part of the Universe is that envelopped by the…
Density perturbations related to structure formations are expected to be different in dissipative and non-dissipative universes, even if the background evolution of the two universes is the same. To clarify the difference between the two…
We investigate the phenomenology of freely expanding fluids, with different material properties, evolving through the Israel-Stewart (IS) causal viscous hydrodynamics, and compare our results with those obtained in the relativistic…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
Thermal interactions are ubiquitous in the cosmos, driving systems toward equilibrium. In this work, we investigate the evolution of thermal states across the early universe, encompassing the inflationary, radiation-dominated (RD), and…
This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…
A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in…
This paper addresses the stability and large-time behavior problem on the perturbations near the hydrostatic balance of the two dimensional Boussinesq system, taking into account vertical dissipation and horizontal thermal diffusion. The…
The essence of the second law of classical thermodynamics is the `entropy principle' which asserts the existence of an additive and extensive entropy function, S, that is defined for all equilibrium states of thermodynamic systems and whose…
In this article, we investigate the thermodynamic stability of the FRW universe for two examples, Tsallis entropy and loop quantum gravity, by considering non-extensive statistical mechanics. The heat capacity, free energy and pressure of…
The irreversible entropy increase described by the second law of thermodynamics is fundamentally tied to thermalization and the emergence of equilibrium. In the first part of our work (Ref: arXiv.2503.04152), we constructed an isolated gas…
We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by…