Related papers: Variational principle for Gibbs point processes wi…
We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state…
When an isolated system is brought in contact with a heat bath its final energy is random and follows the Gibbs distribution -- a cornerstone of statistical physics. The system's energy can also be changed by performing non-adiabatic work…
Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations involving fractional Brownian motions and, as such, their exact value is often…
The classical energy minimization principles of Dirichlet and Thompson are extended as minimization principles to acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency. This is done by building upon…
As no heat effect and mechanical work are observed, we have a simple experimental resolution of the Gibbs paradox: both the thermodynamic entropy of mixing and the Gibbs free energy change are zero during the formation of any ideal…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…
We develop a variational approach at finite temperature that incorporates many-body correlation self-consistently. The grand potential is constructed in terms of Green's function expressed by the variational parameters. We apply this…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: i) Continuity in the first argument, ii) the validity of the data-processing inequality, iii)…
The minimum entropy production principle provides an approximative variational characterization of close-to-equilibrium stationary states, both for macroscopic systems and for stochastic models. Analyzing the fluctuations of the empirical…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
This paper is about Girsanov's theory. It (almost) doesn't contain new results but it is based on a simplified new approach which takes advantage of the (weak) extra requirement that some relative entropy is finite. Under this assumption,…
The perturbation theory with a variational basis is constructed and analyzed.The generalized Gaussian effective potential is introduced and evaluated up to the second order for selfinteracting scalar fields in one and two spatial…
We consider translation-invariant interacting particle systems on the lattice with finite local state space admitting at least one Gibbs measure as a time-stationary measure. The dynamics can be irreversible but should satisfy some mild…
Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on R^d. As reference measures,…
Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct…