Related papers: Bernstein processes, Euclidean Quantum Mechanics a…
Bernstein processes are Brownian diffusions that appear in Euclidean Quantum Mechanics. Knowledge of the symmetries of the Hamilton-Jacobi-Bellman equation associated with these processes allows one to obtain relations between stochastic…
We present some results on Bernstein processes which are Brownian diffusions that appear in Euclidean Quantum Mechanics: We express the distributions of these processes with the help of those of Bessel processes. We then determine two…
We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in…
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. Of particular practical relevance…
Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to…
The Heisenberg uncertainty relation, which links the uncertainties of the position and momentum of a particle, has an important footprint on the quantum behavior of a physical system. Analogous to this principle, we propose that…
In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of…
An intriguing link between a wide range of problems occurring in physics and financial engineering is presented. These problems include the evolution of small perturbations of linear flows in hydrodynamics, the movements of particles in…
We study two different models of optomechanical systems where a temperature gradient between two radiation baths is exploited for inducing self-sustained coherent oscillations of a mechanical resonator. Viewed from a thermodynamic…
Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and…
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a…
In this article we define and investigate statistical operators and an entropy functional for Bernstein stochastic processes associated with hierarchies of forward-backward systems of decoupled deterministic linear parabolic partial…
Quantum correlation, or entanglement, is now believed to be an indispensable physical resource for certain tasks in quantum information processing, for which classically correlated states cannot be useful. Besides information processing,…
After a brief historical perspective, we introduce the key notions of work and heat for quantum systems, to then apply them to quantum engines operating on quantum Otto and Carnot cycles. The irreversible and dissipative character of the…
In this article we provide Bernstein type gradient estimates for two system of local weighted heat type equations with potentials on a weighted Riemannian manifold. We derive all possible cases considering linear potential, exponential…
Quantum thermodynamics aims to explore quantum features to enhance energy conversion beyond classical limits. While significant progress has been made, the understanding of caloric potentials in quantum systems remains incomplete. In this…
Thermodynamics is the phenomenological theory of heat and work. Here we analyze to what extent quantum thermodynamic relations are immune to the underlying mathematical formulation of quantum mechanics. As a main result, we show that the…
We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot statements of the second law of thermodynamics, for situations involving information processing. To this end, we consider an information reservoir (representing, e.g. a…
We study the heat statistics of a quantum Brownian motion described by the Caldeira-Leggett model. By using the path integral approach, we introduce a novel concept of the quantum heat functional along every pair of Feynman paths. This…
Understanding the statistical behavior of the heat in stochastic systems gives us insight about the thermodynamics of such systems. Using the recently proposed Relativistic Stochastic Thermodynamics, we investigate the statistics of the…