Related papers: What defines stationarity in space plasmas
We consider the relative configurational entropy per cell S_Delta as a measure of the degree of spatial disorder for systems of finite-sized objects. It is highly sensitive to deviations from the most spatially ordered reference…
It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence.…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
The Boltzmann-Gibbs celebrated entropy $S_{BG}=-k\sum_ip_i \ln p_i$ is {\it concave} (with regard to all probability distributions $\{p_i\}$) and {\it stable} (under arbitrarily small deformations of any given probability distribution). It…
Recent studies indicate that the configurational entropy is an useful tool to investigate the stability and (or) the relative dominance of states for diverse physical systems. Recent examples comprise the connection between the variation of…
Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the…
A question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume (volume entropy, also known as the Gibbs entropy) or as the logarithm of the density of states…
There are at least two cosmological constants calling for explanation. The first one describes the quasi-de Sitter inflation in the early universe, and the second describes the current acceleration of the universe associated with dark…
The correct modelling of velocity distribution functions for particles in steady-state plasmas is a central element in the study of nuclear fusion and also in the description of space plasmas. In this work, a statistical mechanical…
In a wide class of physical systems, diffeomorphisms in the state space leave the amount of entropy produced per unit time inside the bulk of the system unaffected [M. Polettini et al., 12th Joint European Thermodynamics Conference,…
Stellar models are calculated in the approximation of a uniform density distribution. Variational method was used for determination of the boundary of a stability loss, for stellar masses in the range from 2 up to $10^5$ $M_{\odot}$. The…
Motivated by the doubly special relativity theories and noncommutative spacetime structures, thermodynamical properties of the photon gas in a phase space with compact spatial momentum space is studied. At the high temperature limit, the…
The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the…
From a new rigorous formulation of the general axiomatic foundations of thermodynamics we derive an operational definition of entropy that responds to the emergent need in many technological frameworks to understand and deploy thermodynamic…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
We extend a result of Ledrappier, Hochman, and Solomyak on exact dimensionality of stationary measures for $\text{SL}_2(\mathbb{R})$ to disintegrations of stationary measures for $\text{GL}(\mathbb{R}^d)$ onto the one dimensional foliations…