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The Wasserstein metric is introduced as a probabilistic method to enable quantitative evaluations of LES combustion models. The Wasserstein metric can directly be evaluated from scatter data or statistical results using probabilistic…
A generical formalism for the discussion of Brownian processes with non-constant particle number is developed, based on the observation that the phase space of heat possesses a product structure that can be encoded in a commutative unit…
The approach to curve implicitization through Sylvester and Bezout resultant matrices and bivariate interpolation in the usual power basis is extended to the case of Bernstein-Bezoutian matrices constructed when the polynomials are given in…
We identify and interpret the possible quantum thermal machine regimes with a transverse-field Ising model as the working substance. In general, understanding the emergence of such regimes in a many-body quantum system is challenging due to…
Numerous models have been proposed to describe the Bose-Einstein correlations in multiple particle production processes. In the present paper we describe a generalization, which includes many previous models as special cases and, therefore,…
In the present thesis, we study the heat flow in mesoscopic one-dimensional transport systems. Using the analysis of full counting statistics, we calculate the cumulant generating function of the particle and heat flows and prove its…
The heat-kernel expansion and $\zeta$-regularization techniques for quantum field theory and extended objects on curved space-times are reviewed. In particular, ultrastatic space-times with spatial section consisting in manifold with…
We present a mesoscopic model for thermoelectric phenomena in terms of an interacting particle system, a lattice electron gas dynamics that is a suitable extension of the standard simple exclusion process. We concentrate on electronic heat…
The chemi-ionization (CI) processes in atom-Rydberg-atom collisions are investigated in this contribution. The rate coefficients for CI processes in $\textrm{Li}^{*}(n) + \textrm{Na}$, $\textrm{Li}^{*}(n) + \textrm{Li}$, $\textrm{Na}^{*}(n)…
Tempered fractional Brownian motion is revisited from the viewpoint of reduced fractional Ornstein-Uhlenbeck process. Many of the basic properties of the tempered fractional Brownian motion can be shown to be direct consequences or…
The measurement and interpretation of isotopic yield ratios in heavy ion reactions at intermediate and high energies are discussed and the usefulness of these observables for establishing equilibrium properties and for determining…
The quantum Boltzmann equation, or Fokker-Planck equation, has been used to successfully explain a number of experiments in semiconductor optics in the past two decades. This paper reviews some of the developments of this work, including…
The aim of this paper is to determine lost works in a molecular engine and compare results with macro (classical) heat engines. Firstly, irreversible thermodynamics are reviewed for macro and molecular cycles. Secondly, irreversible…
We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein…
With the approaching second quantum revolution, the study of quantum thermodynamics, particularly heat flow, has become even more relevant for two main reasons. First, understanding heat and other types of noise is essential for protecting…
We study the thermal conductivity in the excitonic insulator using a simple quasi one-dimensional two-band model consisting of electron and hole bands with the Coulomb interactions between these bands. Based on the linear response theory…
From a rigorous multichannel quantum-defect formulation of bimolecular processes, we derive a fully quantal and analytic model for the total rate of exoergic bimolecular reactions and/or inelastic processes that is applicable over a wide…
We present a detailed study of the quantum dissipative dynamics of a charged particle in a magnetic field. Our focus of attention is the effect of dissipation on the low- and high-temperature behavior of the specific heat at constant…
This paper presents review points of mathematical modeling and system identification issues of heat flow process inside a closed box. For system parameter identification, the least squares method is employed and NI Temperature Box is used…
Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $\mathbb{R}^n$. In particular, in the case when $n=2$ they obtained Gaussian…