相关论文: About classical solutions of the path-dependent he…
We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a $\gamma$-H\"older rough path for $\gamma > \frac{1}{3}$. We prove well-posedness of these systems and establish a…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…
We propose a method to evaluate general thermodynamic fluctuations in open quantum systems, based on performing a two-point measurement scheme on the system using dynamics-dependent thermodynamic observables. Our approach allows one to…
A probabilistic construction for the solution of a general class of high order heat-type equations is constructed in terms of the scaling limit of random walks in the complex plane.
We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the…
The problem of statistics of molecular random walks in a classical fluid is analyzed by means of the BBGKY hierarchy of equations reformulated in terms of the Bogolyubov evolution equation for generating functional of many-particle…
In this paper, we establish a large deviation principle for the solutions to the stochastic heat equations with logarithmic nonlinearity driven by Brownian motion, which is neither locally Lipschitz nor locally monotone. Nonlinear versions…
The separation of internal energy into heat and work in quantum thermodynamics is a controversial issue for a long time, and we revisit and solve this problem in this work. It is shown that the Hamiltonian plays dual roles for a quantum…
We prove the existence of solutions for the stochastic differential equation $dX_t=b(t,X_{t-})dZ_t+a(t,X_t)dt, X_0\in\R, t\ge 0,$ with only measurable coefficients $a$ and $b$ satisfying the condition $0<\mu\le |b(t,x)|\le \nu$ and…
Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…
In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are suggested. The time-change process considered…
We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is…
This paper is devoted to path-dependent kinetics equations arising, in particular, from the analysis of the coupled backward - forward systems of equations of mean field games. We present local well-posedness, global existence and some…
We consider three one-dimensional continuous-time Markov processes on a lattice, each of which models the conduction of heat: the family of Brownian Energy Processes with parameter $m$, a Generalized Brownian Energy Process, and the…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
We obtain a new probabilistic representation for the solution of the heat equation in terms of a product for smooth random variables which is introduced and studied in this paper. This multiplication, expressed in terms of the…
We propose an embedding of standard active particle models in terms of two-temperature processes. One temperature refers to an ambient thermal bath, and the other temperature effectively describes ``hot spots,'' i.e., systems with few…
In a simple model of a continuous random walk a particle moves in one dimension with the velocity fluctuating between V and -V. If V is associated with the thermal velocity of a Brownian particle and allowed to be position dependent, the…
In this work, we investigate the one-dimensional heat equation within the framework of Stieltjes calculus. We first consider the equation associated with two fixed derivators and develop a constructive approach to establish the existence of…
Herein, we analyse polytropic processes for an ideal gas within the wider concept of thermal capacity. To answer the question of whether the thermal capacity is a process, path, or state function, we argue that it should be tentatively set…