Emergent pseudo time-irreversibility in the classical many-body system of pair interacting particles

Hydrodynamic density functional theory of simple dissipative fluids

“…respectively, where δ(r) is the d-dimensional Dirac-delta distribution, and d the spatial dimensionality of the problem. The derivation of closed coarse-grained equations for slow variables starts with the derivation of the operator representation of the Hamiltonian equations, which is based on the method of Zaccarelli et al [51] (also used by Archer [47] and Tóth [52,53]). Accordingly, we calculate the Fourier transform of the microscopic densities, differentiate the result w.r.t.…”

“…The dominance of locality is also expected for incompressible liquids and dilute gases for the following reasons. In the former, the density is constant, and therefore ∂ t ρ = 0, while in the latter, the dimensionless equations approximate the kinetic limit: When the length-scale Λ ≡ (m/ρ) 1/d (where ρ is the average mass density of the system) is much larger than the characteristic length-scale of the interaction potential(s), a local theory is recovered [53], and therefore the dimensionless counterpart of σ exc will tend to zero. σ exc is expected to be dominant in case of high density and compressibility, which is characteristic to near-critical fluids.…”

Understanding probability and irreversibility in the Mori-Zwanzig projection operator formalism

“…Second, one could ask what this implies for classical statistical mechanics, which the MZ formalism is also applied to. While in a real physical system one could argue that it is always ultimately described by quantum mechanics 12 , thermodynamic irreversibility is also observed in classical molecular dynamics simulations (Tóth, 2022) that involve no quantum effects of any sort. Moreover, one can apply the MZ formalism (like statistical mechanics in general) also to astrophysical (te Vrugt et al, 2021a) or colloidal (Español & Löwen, 2009) systems, and it is not very plausible that the dynamics of macroscopic colloids or even stars depends on quantum effects.…”

“…More recent discussions can be found in Michel et al (2006) and Dhar and Spohn (2019). Even more recently, Tóth (2022) has investigated via computer simulations whether pseudo-irreversibility is present in a closed many-body system. While the answer turned out to be yes, the precise relaxation behavior was not diffusive as expected, e.g., from Fourier's law.…”