相关论文: A Counter Example to Cercignani's Conjecture for t…

The Boltzmann equation is an integro-differential equation which describes the density function of the distribution of the velocities of the molecules of dilute monoatomic gases under the assumption that the energy is only transferred via…

We present a proposal to relate the de Sitter Conjecture (dSC) to the Covariant Entropy Bound (CEB). By assuming an early phase of accelerated expansion where the CEB is satisfied, we take into account a contribution from extra-dimensions…

We investigate entropic force cosmological models with the possibility of matter creation and energy exchange between the bulk and the horizon of a homogeneous and an isotropic flat Universe. We consider three different kinds of entropy,…

We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…

We present an overview of a recently suggested new model of quantum initial conditions for the Universe in the form of a cosmological density matrix. This density matrix originally suggested in the Euclidean quantum gravity framework turns…

The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational quantum mechanics from well known inference principles -- probability, entropy and information geometry. Although only partially…

We consider the kinetic transport equation that arise in the Boltzmann-Grad limit of the two-dimensional periodic Lorentz Gas. This equation has been obtained by extending the phase space of positions and velocities through the introduction…

One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum…

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a…

We study the degenerate linear Boltzmann equation inside a bounded domain with a generalized diffuse reflection at the boundary and variable temperature, including the Maxwell boundary conditions with the wall Maxwellian or heavy-tailed…

We discuss the grazing collision limit of certain kinetic models of Bose-Einstein particles obtained from a suitable modification of the one- dimensional Kac caricature of a Maxwellian gas without cut-off. We recover in the limit a…

A new coercivity estimate on the spectral gap of the linearized Boltzmann collision operator for multiple species is proved. The assumptions on the collision kernels include hard and Maxwellian potentials under Grad's angular cut-off…

We study the nonreciprocal Cahn-Hilliard model with thermal noise as a prototypical example of a generic class of non-Hermitian stochastic field theories, analyzed in two companion papers [Suchanek, Kroy, Loos, ArXiv:2303.16701 (2023);…

The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, $d\rightarrow\infty$ limit: the localization transition is then expected to be continuous for the…

For the minimally coupled scalar field in Einstein's theory of gravitation we look for the space of solutions within the class of closed Friedmann universe models. We prove that D = 1 or D > 1, where D is the (fractal) dimension of the set…

A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions…

The spatially homogeneous BGK equation is obtained as the limit if a model of a many particle system, similar to Mark Kac's charicature of the spatially homogeneous Boltzmann equation.

Phase transitions are ubiquitous in our three-dimensional world. By contrast most conventional transitions do not occur in infinite uniform two-dimensional systems because of the increased role of thermal fluctuations. Here we explore the…

We study interacting Bose gases of dimensions $2\le d \in \mathbb N$ at zero temperature in a random model known as the Kac-Luttinger model. Choosing the pair-interaction between the bosons to be of a mean-field type, we prove (complete)…

We investigate the construction of chaotic probability measures on the Boltzmann's sphere, which is the state space of the stochastic process of a many-particle system undergoing a dynamics preserving energy and momentum. Firstly, based on…