Evaluation of memory effects at phase transitions and during relaxation processes

Non-Markovian systems out of equilibrium: Exact results for two routes of coarse graining

“…A related question comprises the entropy production in such coarse-grained systems and whether it is possible to connect thermodynamic quantities such as entropy [37,38,50] as discussed intensively in the framework of stochastic thermodynamics [51][52][53] to dynamic coarse-graining, for example via projection operator techniques? We believe that answering these questions would pave the way towards systematic dynamic coarse-graining of non-equilibrium soft matter systems with applications to active microrheology [25,54], active matter [27,51,55], but also non-stationary situations such as crystallization [56], colloid self-assembly [57] or at phase transitions [58] using a non-stationary GLE [22,59].…”

Data-driven Langevin modeling of nonequilibrium processes

“…It is instructive to compare this formulation to our Markovian Langevin approach, also because we adopt below two model problems 29,30 that were previously studied with this GLE. In these studies, the GLE analysis resulted in slowly decaying memory kernels, which appears to question the applicability of a Markovian Langevin model such as the dLE.…”

“…As a potentially more challenging example, we next consider crystal nucleation and growth processes in a compressed liquid of hard spheres, which was recently studied as a test problem for the nonstationary GLE. 30,52 Adopting 16384 hard spheres with mass m and diameter σ and using a time step δt = m/(k B T )σ, Meyer et al 30 first equilibrated the system in a liquid state at a volume fraction η 0 = 0.45. At time t = 0 crystallization is induced by impulsively compressing the system to a vol-ume fraction η = 0.54 by rescaling the simulation box and all positions, and N traj = 580 trajectories of t max = 214 δt length were propagated.…”

“…53 As a one-dimensional reaction coordinate that accounts for the crystallinity of the system, we choose the percentage x of particles that completed crystallization, which is readily calculated from the Q 6 order parameter. 30,53 To get an overview of the nucleation dynamics of the system, Fig. 4a shows the time evolution x(t) of eight sample trajectories.…”

“…As first applications, we demonstrate that the Markovian LE (1) correctly accounts for two nonequilibrium processes recently studied via a nonstationary GLE, 12,13 that is, the enforced dissociation of NaCl in water 29 and the pressure-jump induced nucleation and growth process in a liquid of hard spheres. 30 In both cases, a simple Langevin model is constructed that is shown to reproduce well the underlying MD reference data. As a Langevin-based enhanced sampling strategy, 31 we finally consider the construction of a global Langevin model that accounts for the overall kinetics of the system, obtained from massive parallel computing of short MD trajectories that are per se nonstationary.…”