Related papers: Simplified Derivation of the Non-Equilibrium Proba…
Post-exponential decay of the probability density of a quantum particle leaving a trap can be reproduced accurately, except for interference oscillations at the transition to the post-exponential regime, by means of an ensemble of classical…
A nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a classically driven nonlinear differential equation with dissipation and a semi-classical interpretation of…
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and…
The dissipation function for a system is defined as the natural logarithm of the ratio between probabilities of a trajectory and its time-reversed trajectory, and its probability distribution follows a well-known relation called the…
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
Non-equilibrium steady states (NESS) of Markov processes give rise to non-trivial cyclic probability fluxes. Cycle decompositions of the steady state offer an effective description of such fluxes. Here, we present an iterative cycle…
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in…
A kinetic equation is derived for the phase density of a system of point particles, generating a system of integro-differential equations for distribution functions that have a deterministic meaning. The derivation took into account the…
Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning. In its original formulation it is limited to conservative systems, $\textit{i.e.}$ to…
In this paper, we prove some a priori estimates for a system of partial differential equations arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The unknowns of…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…