Related papers: Bernstein processes, Euclidean Quantum Mechanics a…
We construct default-free interest rate models in the spirit of the well-known Markov funcional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and…
A unified description of i) classical phase transitions and their remnants in finite systems and ii) quantum phase transitions is presented. The ensuing discussion relies on the interplay between, on the one hand, the thermodynamic concepts…
In this paper, we study Ornstein-Uhlenbeck operators with quadratic potentials. We use Hamiltonian formalism to characterise the singularities produced by the potentials by finding explicit geodesics of the operators, and obtain the heat…
Thermalization process of nuclear matter in central fireball region of heavy-ion collisions is investigated by employing an extension model of Boltzmann-Uehling-Uhlenbeck, namely the Van der Waals Boltzmann-Uehling-Uhlenbeck (VdWBUU) model.…
A quasi-static process is realized in a purely quantum-mechanical model which is described by oscillator (or particle) systems having relative-phase interactions. Time development of a mixture of two oscillator (or particle) systems which…
Algebraic methods for solving time dependent Hamiltonians are used to investigate the performance of quantum thermal machines. We investigate the thermodynamic properties of an engine formed by two coupled q-bits, performing an Otto cycle.…
We extend the classical Bernstein inequality to a general setting including Schr{\"o}dinger operators and divergence form elliptic operators on Riemannian manifolds or domains. Moreover , we prove a new reverse inequality that can be seen…
How to introduce thermodynamics to quantum mechanics ? Among from numerous possibilities of solving this task, the simple choice is here: The conventional von Neumann equation deals with a density operator whose probability weights are time…
There is a current interest in quantum thermodynamics in the context of open quantum systems. An important issue is the consistency of quantum thermodynamics, in particular the second law of thermodynamics, i.e., the flow of heat from a hot…
The reheating process in inflationary universe models is considered as an out-of-equilibrium mixture of two interacting and reacting fluids, and studied within the framework of causal, irreversible thermodynamics. The evolution of the…
In this paper, we study the heat equation associated with the Jacobi--Cherednik operator on the real line. We establish some basic properties of the Jacobi--Cherednik heat kernel and heat semigroup. We also provide a solution to the Cauchy…
We sketch some connecting relations involving fractional and quantum calculi, fractal structure, thermodynamics, and quantum mechanics.
Heat kernel coefficients encode the short distance behavior of propagators in the presence of background fields, and are thus useful in quantum field theory. We present a Mathematica program for computing these coefficients and their…
We consider the thermodynamic approach to the description of economic systems and processes. The first and second laws of thermodynamics as applied to economic systems are derived and analyzed. It is shown that there is a deep analogy…
We show how using a special relativistic kinetic equation with a BGK- like collision operator the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly…
We consider thermodynamic properties, e.g. specific heat, magnetic susceptibility, of alternating Heisenberg spin chains. Due to a hidden Ising symmetry these chains can be decomposed into a set of finite chain fragments. The problem of…
In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine…
Advantages of quantum effects in several technologies, such as computation and communication, have already been well appreciated, and some devices, such as quantum computers and communication links, exhibiting superiority to their classical…
Multivariate Bessel and Jacobi processes describe Calogero-Moser-Sutherland particle models. They depend on a parameter $k$ and are related to time-dependent classical random matrix models like Dysom Brownian motions, where $k$ has the…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an…