Related papers: Bernstein processes, Euclidean Quantum Mechanics a…
In this paper we address again the problem of the connection between multitime Brownian sheet and heat type PDEs. The main results include: the volumetric character of the solutions of the forward (backward) diffusion-like PDEs; the forward…
We present a theory that combines the framework of irreversible thermodynamics with modified integral theorems to model arbitrarily curved and deforming membranes immersed in bulk fluid solutions. We study the coupling between the mechanics…
We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group $\mathbb{G}$ and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on $\mathbb{G}$.…
This Colloquium is a fast journey through the build-up of key thermodynamical concepts, i.e. work, heat and irreversibility -- and how they relate to information. Born at the time of industrial revolution to optimize the exploitation of…
The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a trade-off relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines.…
A dissipative mechanism is presented, which emerges in generic interacting quantum field systems and which leads to robust warm inflation. An explicit example is considered, where using typical parameter values, it is shown that…
Four-dimensional Euclidean spaces that solve Einstein's equations are interpreted as WKB approximations to wavefunctionals of quantum geometry. These spaces are represented graphically by suppressing inessential dimensions and drawing the…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
The aim of this book chapter is to indicate how quantum phenomena are affecting the operation of microscopic thermal machines, such as engines and refrigerators. As converting heat to work is one of the fundamental concerns in…
The Mullins effect is a common name for a family of intriguing inelastic responses of various solid materials, in particular filled rubbers. Given the importance of the Mullins effect, there have been many attempts to develop mathematical…
A method for integrating the chemical equations associated with nuclear combustion at high temperature is presented and extensively checked. Following the idea of E. M\"uller, the feedback between nuclear rates and temperature was taken…
We investigate the temperature uncertainty relation in nonequilibrium probe-based temperature estimation process. We demonstrate that it is the fluctuation of heat that fundamentally determines temperature precision through the…
We study the energy exchange between two bosonic systems that interact via bilinear transformations in the mode operators. The first mode is considered as the thermodynamic system, while the second is regarded as the bath. This work finds…
Invoking a rather simple semigroup approach, we refine the recent qualitative properties of Euclidean heat content obtained by van den Berg and Gittins.
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation. We prove the appropriate generalizations…
We present an explicit correspondence between quantum mechanics and the classical theory of irreversible thermodynamics as developed by Onsager, Prigogine et al. Our correspondence maps irreversible Gaussian Markov processes into the…
There exist two formulations for quantum heat engine that models an energy transfer between two microscopic systems. One is semi-classical scenario, and the other is full quantum scenario. The former is formulated as a unitary evolution for…
We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction…
Isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for…