Related papers: An Interesting Class of Partial Differential Equat…
We study ergodic properties of certain piecewise smooth two-dimensional systems by constructing countable Markov partitions. Using thermodynamic formalism we prove exponential decay of correleations.
Partial differential equations for the electric potential at finite temperature, taking into account the thermal Euler-Heisenberg contribution to the electromagnetic Lagrangian are derived. This complete temperature dependence introduces…
In this paper, we establish a large deviation principle for the conservative stochastic partial differential equations, whose solutions are related to stochastic differential equations with interaction. The weak convergence method and the…
In this paper we study the representation of partial differential equations (PDEs) as abstract differential-algebraic equations (DAEs) with dissipative Hamiltonian structure (adHDAEs). We show that these systems not only arise when there…
We study the properties of mixed states obtained from eigenstates of many-body lattice Hamiltonians after tracing out part of the lattice. Two scenarios emerge for generic systems: (i) the diagonal entropy becomes equivalent to the…
We present initially the motivation, definition and basic properties of differential equations with proportional delay. In the last Section we present open problems.
An overview is given of recent advances in the nonequilibrium statistical mechanics of quantum systems and, especially, of time-reversal symmetry relations that have been discovered in this context. The systems considered are driven out of…
In this paper we investigate some properties, including causality, of a particular class of relativistic dissipative fluid theories of divergence type. This set is defined as those theories coming from a statistical description of matter,…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a non-vanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical…
We reconsider general aspects of Galilean-invariant thermal field theory. Using the proposal of our companion paper, we recast non-relativistic hydrodynamics in a manifestly covariant way and couple it to a background spacetime. We examine…
The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum…
The Onsager's conjecture has two parts: conservation of energy, if the exponent is larger than $1/3$ and the possibility of dissipative Euler solutions, if the exponent is less or equal than $1/3$. The paper proves half of the conjecture,…
We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first one is deduced from a balance law for entropy and…
Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle…
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…
The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We consider a one-dimensional exclusion dynamics in mild contact with boundary reservoirs. In the diffusive scale, the particles' density evolves as the solution of the heat equation with non-linear Robin boundary conditions. For…
Some models for developed turbulence are considered; they are shown to obey a large fluctuations theorem, and one among them also obeys a response reciprocity relation of Onsager's type. This illustrates and extends ideas and techniques…