Related papers: Heat trace asymptotics of a time dependent process

We investigate the short-time expansion of the heat kernel of a Laplace type operator on a compact Riemannian manifold and show that the lowest order term of this expansion is given by the Fredholm determinant of the Hessian of the energy…

The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…

We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant…

Given a real reductive group $G$, the purpose of this paper is to show an asymptotic formula of the large-time behavior of the $G$-trace of the heat operator on the associated symmetric spaces. Together with Carmona's proof on Vogan's…

This study utilizes mathematical modeling to offer computational insights into biological heat transfer within elastic skin tissues. This heat transfer is driven by a moving heat source that relies on various relaxation times. Time delay…

This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…

This work introduces novel numerical algorithms for computational quantum mechanics, grounded in a representation of the Laplace operator -- frequently used to model kinetic energy in quantum systems -- via the heat semigroup. The key…

Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special…

We study the asymptotic behaviour of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions. Assuming the existence of a complete asymptotic series we…

Recently proposed nonlocal and nonperturbative late time behavior of the heat kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is dominated by two terms one of which represents a trivial covariantization of the…

This article provides a functional analytical framework for boundary integral equations of the heat equation in time-dependent domains. More specifically, we consider a non-cylindrical domain in space-time that is the $C^2$-diffeomorphic…

Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend…

We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…

We study trace functions on the form $ t\to\tr f(A+tB) $ where $ f $ is a real function defined on the positive half-line, and $ A $ and $ B $ are matrices such that $ A $ is positive definite and $ B $ is positive semi-definite. If $ f $…

Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to…

We consider time periodic Hamiltonians with complex potentials on the lattice and determine trace formulas. As a corollary we estimate eigenvalues of the quasienergy operator in terms of the norm of potentials.

We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show that the…

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…

We propose a theory based on simple physical arguments that describes a non equilibrium steady-state by a temperature-like parameter (an "effective temperature"). We show how one can predict the effective temperature as a function of the…

We consider a model of heat conduction which consists of a finite nonlinear chain coupled to two heat reservoirs at different temperatures. We study the low temperature asymptotic behavior of the invariant measure. We show that, in this…