Related papers: The thermodynamic limit of the Whitham equations
We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg-de Vries (KdV) equation in the special "condensate" limit. We prove that in this limit the integro-differential kinetic equation for the spectral density…
Macroscopic dynamics of soliton gases can be analytically described by the thermodynamic limit of the Whitham equations, yielding an integro-differential kinetic equation for the density of states. Under a delta-functional ansatz, the…
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…
Limiting structure of thermodynamic functions of gaseous plasmas is under consideration in the limit of low temperature and density. The remarkable tendency, that was claimed previously [High Temp. 19, 799 (1981)], is carried to extreme. In…
The present effort addresses the question about the existence of a well-defined thermodynamic limit for the astrophysical systems with the following power law form: to tend the number of particles, N, the total energy, E, and the…
The existence of the thermodynamic limit in spin systems with short- and long-range interactions is established. We consider the infinite-volume limit with a fixed shape of the system. The variational expressions of the entropy density and…
We present a general framework for thermodynamic limits and its applications to a variety of models. In particular we will identify criteria such that the limits are uniform in a parameter. All results are illustrated with the example of…
Assuming that Bogoliubov's theory of weakly interacting dilute Bose gas defines a self-consistent model Hamiltonian, we investigate its thermodynamic limit as we take the volume to infinity. The infinite volume is taken via a sequence of…
We construct a definition of the weak solution to KdV type equations with small dispersion admitting the zero dispersion limit for soliton-like solutions. Using this definition, we obtain a system of equations (the limit problem as the…
The hydrodynamic limit of a one dimensional kinetic model describing chemotaxis is investigated. The limit system is a conservation law coupled to an elliptic problem for which the macroscopic velocity is possibly discontinuous. Therefore,…
An exact analytical solution of the statistical multifragmentation model is found in thermodynamic limit. The model exhibits a 1-st order phase transition of the liquid-gas type. The mixed phase region of the phase diagram, where the gas of…
Limiting structure of thermodynamic functions of gaseous plasmas is under consideration in the limit of zero temperature and density. Remarkable tendency, which was claimed previously (Iosilevskiy and Gryaznov, 1985) is carried to extreme.…
The macroscopic zero-temperature behavior of weakly- incommensurate systems in one dimension is described in terms of solitons. The soliton density n obeys equations displaying several types of singular interface-like solutions: (i)…
Quantum speed limits are rigorous estimates on how fast a state of a quantum system can depart from the initial state in the course of quantum evolution. Most known quantum speed limits, including the celebrated Mandelstam-Tamm and…
We have considered a model of a small finite system with internal particles and surface degrees of freedom. All the main statistical distributions were explicitly obtained, on a pre thermodynamic limit basis. The concept of temperature or…
We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported…
We investigate the thermodynamic limit for the cubic-quintic Schr\"{o}dinger model as the size of the domain tends to infinity with fixed density $\rho= N/|\mathcal{D}|$, where $N$ denotes particle number and $|\mathcal{D}|$ denotes the…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
We study the energy spectrum of tight-binding Hamiltonian for regular hyperbolic tilings. More specifically, we compute the density of states using the continued-fraction expansion of the Green function on finite-size systems with more than…
We derive the dark energy fluid equation of state $P = -\epsilon = {\rm const.}$ as an extremum of entropy, subject to the Hamiltonian constraint of General Relativity. However, we identify perturbations that can render this extremum an…