The Five Problems of Irreversibility

Vrugt, Michael te

doi:10.48550/arxiv.2004.01276

Cited by 3 publications

(9 citation statements)

References 41 publications

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“…This general theory allows to derive DDFT if the relevant variable is the one-particle density (60), such that Eq. ( 96) provides a dynamic equation for ρ( r, t) = ρ( r, t) .…”

Section: Via Projection Operator Formalismmentioning

confidence: 99%

“…In equilibrium DFT, the one-body density gives, as discussed in Section 2.2, all relevant information about the system. For a system initially out of equilibrium, however, this is not the case due to an additional dependence on the initial condition [60,130]. Consequently, it is possible that a nonequilibrium system has an equilibrium density profile that minimizes the free energy functional, but a nonequilibrium correlation.…”

Section: Limitations Of Ddftmentioning

confidence: 99%

“…Among the central topics of nonequilibrium statistical mechanics is the question how and why systems approach a state of thermodynamic equilibrium [60,389]. The tendency to approach equilibrium is often associated with the second law of thermodynamics (see Ref.…”

Section: Approach To Equilibriummentioning

confidence: 99%

“…It has also found a significant number of applications, ranging from "typical" ones, such as the derivation of phase field crystal (PFC) models [44], phase separation [14], and solidification [45], to more exotic ones, such as cancer growth [46] or quantum hydrodynamics [47]. DDFT is now used in many areas of physics, as well as in related subjects such as biology [48][49][50], chemistry [51][52][53], materials science [54][55][56], engineering [57], mathematics [58,59], and philosophy [60]. This diversity arises, since the problem of finding a useful and accurate description of the collective dynamics in many-particle systems is of importance in a large number of areas in and beyond physics.…”

Section: Introductionmentioning

confidence: 99%

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Classical dynamical density functional theory: from fundamentals to applications

Vrugt

Löwen

Wittkowski

2020

Advances in Physics

189

220

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Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems. Originally developed for the treatment of simple and complex fluids, DDFT is now applied in fields as diverse as hydrodynamics, materials science, chemistry, biology, and plasma physics. In this review, we give a broad overview over classical DDFT. We explain its theoretical foundations and the ways in which it can be derived. The relations between the different forms of deterministic and stochastic DDFT as well as between DDFT and related theories, such as quantum-mechanical time-dependent DFT, mode coupling theory, and phase field crystal models, are clarified. Moreover, we discuss the wide spectrum of extensions of DDFT, which covers methods with additional order parameters (like extended DDFT), exact approaches (like power functional theory), and systems with more complex dynamics (like active matter). Finally, the large variety of applications, ranging from fluid mechanics and polymer physics to solidification, pattern formation, biophysics, and electrochemistry, is presented.

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“…This general theory allows to derive DDFT if the relevant variable is the one-particle density (60), such that Eq. ( 96) provides a dynamic equation for ρ( r, t) = ρ( r, t) .…”

Section: Via Projection Operator Formalismmentioning

confidence: 99%

Section: Limitations Of Ddftmentioning

confidence: 99%

Section: Approach To Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Classical dynamical density functional theory: from fundamentals to applications

Vrugt

Löwen

Wittkowski

2020

Advances in Physics

189

220

View full text Add to dashboard Cite

show abstract

“…Although it is made in almost all practical cases, the Markovian approximation is not innocent. From a foundational perspective, it introduces the thermodynamic irreversibility not present in the time-reversal-invariant microscopic laws of physics [66]. In the Markovian limit, an H-theorem corresponding to an increase of entropy can be proven [67,68].…”

Section: Causal Field Theoriesmentioning

confidence: 99%

Jerky active matter: a phase field crystal model with translational and orientational memory

Vrugt,

Jeggle,

Wittkowski

2021

Preprint

Self Cite

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Most field theories for active matter neglect effects of memory and inertia. However, recent experiments have found inertial delay to be important for the motion of self-propelled particles. A major challenge in the theoretical description of these effects, which makes the application of standard methods very difficult, is the fact that orientable particles have both translational and orientational degrees of freedom which do not necessarily relax on the same time scale. In this work, we derive the general mathematical form of a field theory for soft matter systems with two different time scales. This allows to obtain a phase field crystal model for polar (i.e., nonspherical or active) particles with translational and orientational memory. Notably, this theory is of third order in temporal derivatives and can thus be seen as a spatiotemporal jerky dynamics. We obtain the phase diagram of this model, which shows that, unlike in the passive case, the linear stability of the liquid state depends on the damping coefficients. Moreover, we investigate sound waves in active matter. It is found that, in active fluids, there are two different mechanisms for sound propagation. For certain parameter values and sufficiently high frequencies, sound mediated by polarization waves experiences less damping than usual passive sound mediated by pressure waves of the same frequency. By combining the different modes, acoustic frequency filters based on active fluids could be realized.

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Projection operators in statistical mechanics: a pedagogical approach

Vrugt

Wittkowski

2020

Eur. J. Phys.

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The Mori-Zwanzig projection operator formalism is one of the central tools of nonequilibrium statistical mechanics, allowing to derive macroscopic equations of motion from the microscopic dynamics through a systematic coarse-graining procedure. It is important as a method in physical research and gives many insights into the general structure of nonequilibrium transport equations and the general procedure of microscopic derivations. Therefore, it is a valuable ingredient of basic and advanced courses in statistical mechanics. However, accessible introductions to this methodin particular in its more advanced forms -are extremely rare. In this article, we give a simple and systematic introduction to the Mori-Zwanzig formalism, which allows students to understand the methodology in the form it is used in current research. This includes both basic and modern versions of the theory. Moreover, we relate the formalism to more general aspects of statistical mechanics and quantum mechanics. Thereby, we explain how this method can be incorporated into a lecture course on statistical mechanics as a way to give a general introduction to the study of nonequilibrium systems. Applications, in particular to spin relaxation and dynamical density functional theory, are also discussed. * Corresponding author: raphael.wittkowski@uni-muenster.de 1 Active particles are particles that convert energy into directed motion. A good example are swimming microorganisms [1]. 2 This is not possible for active systems [7].

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The Five Problems of Irreversibility

Cited by 3 publications

References 41 publications

Classical dynamical density functional theory: from fundamentals to applications

Classical dynamical density functional theory: from fundamentals to applications

Jerky active matter: a phase field crystal model with translational and orientational memory

Projection operators in statistical mechanics: a pedagogical approach

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