Related papers: Tropical thermodynamic formalism
We study the equilibrium and near-equilibrium properties of a holographic five-dimensional model consisting of Einstein gravity coupled to a scalar field with a non-trivial potential. The dual four-dimensional gauge theory is not conformal…
We consider 1D integrable systems supporting ballistic propagation of excitations, perturbed by a localised defect that breaks most conservation laws and induces chaotic dynamics. Focusing on classical systems, we study an…
We consider the random point processes on a measure space X defined by the Gibbs measures associated to a given sequence of N-particle Hamiltonians H^{(N)}. Inspired by the method of Messer-Spohn for proving concentration properties for the…
A plausible mechanism of thermalization in isolated quantum systems is based on the strong version of the eigenstate thermalization hypothesis (ETH), which states that all the energy eigenstates in the microcanonical energy shell have…
Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties…
We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at…
Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early…
We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…
We study convergence rates of the Trotter splitting $e^{A+L} = \lim_{n \to \infty} (e^{L/n} e^{A/n})^n$ in the strong operator topology. In the first part, we use complex interpolation theory to treat generators $L$ and $A$ of contraction…
Given an elliptic operator $L= - \mathrm{div} (A \nabla \cdot)$ subject to mixed boundary conditions on an open subset of $\mathbb{R}^d$, we study the relation between Gaussian pointwise estimates for the kernel of the associated heat…
We address the issue of extending thermodynamics to nonequilibrium steady states. Using driven stochastic lattice gases, we ask whether consistent definitions of an effective chemical potential mu, and an effective temperature T_e, are…
In this paper, we consider the Cauchy problem to the TROPIC CLIMATE MODEL derived by Frierson-Majda-Pauluis in [Comm. Math. Sci, Vol. 2 (2004)] which is a coupled system of the barotropic and the first baroclinic modes of the velocity and…
The standard Large Deviation Theory (LDT) is mathematically illustrated by the Boltzmann-Gibbs factor which describes the thermal equilibrium of short-range-interacting many-body Hamiltonian systems, the velocity distribution of which is…
We show that heat defines a gauge connection on a line bundle over work configurations. Vanishing curvature is equivalent to the local existence of entropy and temperature functions such that heat can be expressed as $TdS$. A conjecture of…
The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable…
We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…
We consider a class of homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting…
We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…
Denote by $X$ a Banach space and by $T : X \to X$ a bounded linear operator with non-trivial kernel satisfying suitable conditions. We consider the concepts of entropy - for $T$-invariant probability measures - and pressure for H\"older…
A new method of constructing a weak coupling expansion of two dimensional (2D) models with an unbroken continuous symmetry is developed. The method is based on an analogy with the abelian XY model, respects the Mermin-Wagner (MW) theorem…