Incomplete relaxation in a two-mass one-dimensional self-gravitating system

Yawn, Kenneth R.; Miller, Bruce N.

doi:10.1103/physreve.68.056120

Cited by 36 publications

(43 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand if dynamics is adiabatic -which is the case for the initial particle distributions that satisfy GVC -then α = 0.4, which is close to the exponent found for non-interacting particles. It will be interesting to explore how universal are these exponents by studying other long range systems, such as magnetically confined plasmas [15] or self-gravitating clusters [16][17][18][19]. The fact that the paramagnetic resonances and chaotic dynamics diminish significantly the entropy production time suggests that for short range interacting systems, for which dynamics is highly non-linear and chaotic, the exponent α → 0, and the entropy production will take place on a microscopic time scale even in the thermodynamic limit.…”

Section: Discussionmentioning

confidence: 99%

Entropy production in systems with long range interactions

Pakter

Levin

2017

J. Stat. Mech.

View full text Add to dashboard Cite

On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville's theorem for Hamiltonian systems and appears to contradict the second law of thermodynamics. In reality, however, there is no problem since the thermodynamic entropy should be associated with the Boltzmann entropy, which for non-equilibrium systems is different from Gibbs entropy. The Boltzmann entropy accounts for the microstates which are not accessible from a given initial condition, but are compatible with a given macrostate. In a sense the Boltzmann entropy is a coarse grained version of the Gibbs entropy and will not decrease during the dynamical evolution of a macroscopic system. In this paper we will explore the entropy production for systems with long range interactions. Unlike for short range systems, in the thermodynamic limit, the probability density function for these systems decouples into a product of one particle distribution functions and the coarse grained entropy can be calculated explicitly. We find that the characteristic time for the entropy production scales with the number of particles as N α , with α > 0, so that in the thermodynamic limit entropy production takes an infinite amount of time. * pakter@if.ufrgs.br † levin@if.ufrgs.br 2

show abstract

Section: Discussionmentioning

confidence: 99%

Entropy production in systems with long range interactions

Pakter

Levin

2017

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…where is a softening parameter introduced to avoid the zero distance divergence in the pair interaction potential, and the infinite sheet model in three dimensions, describing N infinite planes with constant mass density with motion only along the x axis [43]:…”

Section: Dynamics Of Correlations and The Vlasov Equationmentioning

confidence: 99%

Dynamics and physical interpretation of quasistationary states in systems with long-range interactions

et al. 2014

View full text Add to dashboard Cite

Although the Vlasov equation is used as a good approximation for a sufficiently large N , Braun and Hepp have showed that the time evolution of the one particle distribution function of a N particle classical Hamiltonian system with long range interactions satisfies the Vlasov equation in the limit of infinite N . Here we rederive this result using a different approach allowing a discussion of the role of inter-particle correlations on the system dynamics. Otherwise for finite N collisional corrections must be introduced. This has allowed the a quite comprehensive study of the Quasi Stationary States (QSS) but many aspects of the physical interpretations of these states remain unclear. In this paper a proper definition of timescale for long time evolution is discussed and several numerical results are presented, for different values of N . Previous reports indicates that the lifetimes of the QSS scale as N 1.7 or even the system properties scales with exp(N ). However, preliminary results presented here shows indicates that time scale goes as N 2 for a different type of initial condition. We also discuss how the form of the inter-particle potential determines the convergence of the N -particle dynamics to the Vlasov equation. The results are obtained in the context of following models: the Hamiltonian Mean Field, the Self Gravitating Ring Model, and a 2-D Systems of Gravitating Particles. We have also provided information of the validity of the Vlasov equation for finite N , i. e. how the dynamics converges to the mean-field (Vlasov) description as N increases and how inter-particle correlations arise.

show abstract

“…Incomplete (or partial) equilibrium states [2,3] are in this respect a remarkable exception, since in these cases concepts of equilibrium statistical mechanics can be used to describe nonequilibrium situations. Incomplete equilibrium states arise when different parts of the system themselves reach a state of equilibrium long before they equilibrate with each other [2].…”

mentioning

confidence: 99%

“…Our theoretical approach, based on the idea of incomplete equilibrium [2], given the quasi-stationary values of the order parameter and the temperature, allows one to calculate the other thermodynamic quantities such as the energy of the system and its fluctuations (i.e., the specific heat). We expect the present approach to be significant for nonequilibrium systems displaying stationarity or quasi-stationarity [3,5,8,13,19,20] concomitantly with a kinetic theory based on the Vlasov or BalescuLenard equations [4].…”

mentioning

confidence: 99%

Incomplete Equilibrium in Long-Range Interacting Systems

Baldovin

Orlandini

2006

Phys. Rev. Lett.

View full text Add to dashboard Cite

We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasistationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution, we find that the Central Limit Theorem implies the Boltzmann expression in Gibbs' Γ-space. We identify the nonequilibrium sub-manifold of Γ-space characterizing the anomalous behavior and show that by restricting the Boltzmann-Gibbs approach to this sub-manifold we obtain the statistical mechanics of the quasi-stationary states.PACS numbers: 05.70.Ln, In comparison with its equilibrium counterpart, nonequilibrium statistical mechanics does not rely on universal notions, like the ensembles ones, through which one can handle large classes of physical systems [1]. Incomplete (or partial) equilibrium states [2,3] are in this respect a remarkable exception, since in these cases concepts of equilibrium statistical mechanics can be used to describe nonequilibrium situations. Incomplete equilibrium states arise when different parts of the system themselves reach a state of equilibrium long before they equilibrate with each other [2]. The classical understanding on how a system approaches equilibrium is based on the short time-scale collisions mechanism which links any initial condition to the statistical equilibrium. For longrange interacting systems, this picture is not valid anymore since the time-scale for microscopic collisions diverges with the range of the interactions. This implies that the Boltzmann equation must be substituted with other approximations such as the Vlasov or the BalescuLenard equations [4], where the interparticle correlations are negligible or almost negligible and a nonequilibrium initial configuration could stay frozen or almost frozen for a very long time. This applies, e.g., to gravitational systems, Bose-Einstein condensates and plasma physics [5]. Due to the physical relevance of long-range interacting systems and to the privileged position of incomplete equilibrium states in nonequilibrium statistical mechanics, it is important to investigate whether the notion of incomplete equilibrium plays an important role in understanding the nonequilibrium properties of these systems.Recently we showed [6] that nonequilibrium states in which the value of macroscopic quantities remains stationary or quasi-stationary for reasonably long time (quasi-stationary states -QSSs) are important, e.g., for experiments, since they appear even when the long-range system exchanges energy with a thermal bath (TB). Using the same paradigmatic long-range interacting system of Ref.[6], the Hamiltonian Mean Field (HMF) model [7], here we discuss the Gibbs' Γ-space statistical mechan- * Electronic address: baldovin@pd.infn.it, orlandin@pd.infn.it ics description of the QSSs in a canonical ensemble perspective. We identify the nonequilibrium sub-manifold of Γ-space within which the quasi-stationary dynamics is confined and we show that the Boltzmann-Gibbs (BG) approach, restricted t...

show abstract

Incomplete relaxation in a two-mass one-dimensional self-gravitating system

Cited by 36 publications

References 28 publications

Entropy production in systems with long range interactions

Entropy production in systems with long range interactions

Dynamics and physical interpretation of quasistationary states in systems with long-range interactions

Incomplete Equilibrium in Long-Range Interacting Systems

Contact Info

Product

Resources

About