By means of the concepts dissipative stability and stochastic realizability, phenomenon ergodicity breaking observed in Generalized Langevin Equations (GLEs) presence nonvanishing friction factors [Phys. Rev. E 83, 062102 (2011)1539-375510.1103/PhysRevE.83.062102] can be properly explained: it occurs at boundary region stability; those cases, this coincides with that realizability. This is case Plyukhin model considers a generalized Debye kernel. In kernels characterized by real-valued...

Using the initial-value formulation, a dynamic theory for systems evolving according to generalized Langevin equation is developed, providing conditions on existence of equilibrium behavior and its fluctuation-dissipation implications. For fulfilling property local realizability, that all practical purposes corresponds postulate Markovian embedding, physical constraints, expressed in form dissipative stability stochastic realizability are derived. If these two properties met, Kubo...

Abstract This article extends the fluctuation-dissipation analysis to generic complex fluids in confined geometries and all cases hydromechanic fluid-interaction kernels may depend on particle position. represents a completely new way of enforcing theory just because primary target is derive an explicit functional expression for force (unaccessible from hydrodynamic analysis) fundamental thermodynamic principles at equilibrium (while classical Kubo memory are explicitly known, stemming mean-field...

Context. The Sun is a privileged laboratory of stellar evolution, thanks to the quality and complementary nature available constraints. Using these observations, we are able draw detailed picture its internal structure dynamics which form basis successes solar modelling. Amongst such constraints, depletion lithium beryllium key tracers required efficiency extent macroscopic mixing just below convective envelope. Thanks revised determinations abundances, may use them in conjunction with other...

The article analyzes some new results that are emerging from highly resolved experimental analysis of Brownian trajectories, addressing their deep connection with the hydrodynamic modeling in light resolving paradoxes infinite speed propagation fields, which is intrinsic to assumption incompressibility liquids and parabolic nature equations. key quantity added mass its emergence as a consequence physically consistent extension regularity properties hydrodynamic-thermal fluctuations (logic)....

We analyze the statistical properties of radiative transitions for a molecular system possessing discrete, equally spaced, energy levels, interacting with thermal radiation at constant temperature. A fluctuation-dissipation theorem is derived and particle velocity distribution analyzed. It shown analytically that, neglecting collisions, function cannot be Gaussian, as equilibrium value kurtosis κ different from κ=3. Maxwellian can recovered in limit small friction.

Starting from the analysis of lack positivity Cattaneo heat equation, this work addresses thermodynamic relevance constraint in irreversible thermodynamics, that is at least as significant entropic constraints. The fulfillment condition hyperbolic models leads to parametrization concentration fields with respect internal variables associated microscopic dynamics. Using Brownian motion theory a landmark example for deriving macroscopic transport equations particle/molecular level, we discuss...

The Central Limit Theorem stands as a milestone in probability theory and statistical physics, the privileged, if not unique, universal route to normal distributions. This article addresses describes several other alternative routes Gaussianity, stemming from physical interactions, related particle-particle radiative particle–photon elementary processes. concept of conservative mixing transformations random ensembles is addressed, it represents main distributional Gaussianity classical...

Starting from the analysis of lack positivity Cattaneo heat equation, article addresses thermodynamic relevance constraint in irreversible thermodynamics, than is at least as important entropic constraints. The fulfillment this condition hyperbolic models leads to parametrization concentration fields with respect internal variables associated microscopic dynamics. Using Brownian motion theory a landmarking example for deriving macroscopic transport equations particle/molecular level, we...

A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations (CMT) in ensembles random vector-valued variables, is proposed. This completely different from additive mechanism characterizing application Central Limit Theorem, as it based on iteration a transformation preserving ensemble variance. Gaussianity emerges "supergeneric" property statistics, case energy constraint quadratic norm variables. result puts light occurrence equilibrium Gaussian...

The phenomenon of ergodicity breaking stochastic dynamics governed by Generalized Langevin Equations (GLE) in the presence well-behaved exponentially decaying dissipative memory kernels, recently investigated many authors (Phys. Rev. E {\bf 83} 062102 2011; Phys. 98} 062140 2018; Eur. J. B 93} 184 2020), finds, dynamic theory GLE, its simple and natural explanation, related to concept stability. It is shown that occurrence breakdown for kernels falls, general, ouside region realizability,...

Using the initial-value formulation, a dynamic theory for systems evolving according to Generalized Langevin Equation is developed, providing more restrictive conditions on existence of equilibrium behavior and its fluctuation-dissipation implications. For fulfilling property local realizability, that all practical purposes corresponds postulate Markovian embedding, physical constraints, expressed in form dissipative stability stochastic realizability are derived. If these two properties...

his article extends the fluctuation-dissipation analysis to generic complex fluids in confined geometries and all cases hydromechanic fluid-interaction kernels may depend on particle position. This represents a completely new way of enforcing theory just because primary target is derive an explicit functional expression for force (that unavailable from linear hydrodynamic theory) fundamental thermodynamic principles at equilibrium (while classical Kubo memory are explicitly known, stemming...

The article provides a unitary and complete solution to the fluctuation-dissipation relations for particle hydromechanics in generic fluid, accounting hydrodynamic fluid-particle interactions (including arbitrary memory kernels description of dissipative fluid inertial effects) linear regimes, via concepts fluctuational patterns. This is achieved by expressing as superposition exponentially decaying modes. Given structure interaction with internal degrees freedom, assuming representation...

The analysis of fluctuation-dissipation relations developed in Giona et al. (2024) for particle hydromechanics is extended to stochastic forcings alternative Wiener processes, with the aim addressing occurrence Gaussian equilibrium densities or alternatively breaking paradigm at equilibrium. Preliminarly, it discussed how determination fluctuational patterns starting from approach Markov processes practically unfeasible, and moment provides simplest way achieve it. We show existence an...

The fluctuation-dissipation theory is grounded on the Langevin condition expressing local independence between thermal force and particle velocity history. Upon hydrodynamic grounds, it reasonable to relax this in order account for correlated fluid fluctuations, especially case of liquids, consistently with inclusion acoustic effects finite speed propagation internal shear stresses. We show that introduction stochastic processes basic fluctuational patterns defined Giona et al. (2024),...

A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles random vector-valued variables, is proposed. This completely different from additive mechanism characterizing application Central Limit Theorem, as it based on iteration a transformation preserving ensemble variance. Gaussianity emerges ``supergeneric'' property statistics, case energy constraint quadratic norm variables. result puts light occurrence equilibrium Gaussian...

We analyze the statistical properties of radiative transitions for a molecular system possessing discrete, equally spaced, energy levels, interacting with thermal radiation at constant temperature. A fluctuation-dissipation theorem is derived and particle velocity distribution analyzed. It shown analytically that, neglecting collisions, function cannot be Gaussian, as equilibrium value kurtosis $\kappa$ different from $\kappa=3$. Maxwellian can recovered in limit small friction.

We propose a general stochastic formalism for describing the evolution of chemical reactions involving finite number molecules. This approach is consistent with statistical analysis based on Chemical Master Equation, and provides formal setting existing algorithmic approaches (Gillespie algorithm). Some practical advantages this formulation are addressed, several examples discussed pointing out connection quantum transitions (radiative interactions).

The stochastic modelling of chemical physical processes is essentially based on a coarse-grained formulation fluctuations, usually described by means Wiener processes. By taking the paradigmatic example reaction kinetics, we propose simple representation microscopic dynamics grounded use distributional derivatives counting that account for elementary reactive events. This approach consistent with statistical analysis Chemical Master Equation, and provides formal setting existing algorithmic...