Time-reversible dissipative ergodic maps

Hoover, William G.; Kum, Oyeon; Posch, Harald A.

doi:10.1103/physreve.53.2123

Cited by 33 publications

(25 citation statements)

References 15 publications

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“…MDM can be a powerful tool for studying non-Boltzmann relaxation phenomena in more or less dense media. Some nonequilibrium processes have already been studied with MDM, for example, in [14,23,[34][35][36][37][38].…”

Section: Boltzmann and Non-boltzmann Relaxationmentioning

confidence: 99%

Stochastic and dynamic properties of molecular dynamics systems: Simple liquids, plasma and electrolytes, polymers

Norman¹,

Stegaĭlov²

2002

Computer Physics Communications

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Section: Boltzmann and Non-boltzmann Relaxationmentioning

confidence: 99%

Stochastic and dynamic properties of molecular dynamics systems: Simple liquids, plasma and electrolytes, polymers

Norman¹,

Stegaĭlov²

2002

Computer Physics Communications

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“…This map turns out to be ergodic, without stable fixed points, and to show the same type of topological behavior exhibited by the driven Lorentz Gas (Galton Board) example of Section 2, the formation of attractor -repellor pairs with a reduced information dimension [21]. Attractors generated with this map are shown in Figures 8 for various values of the control parameter rn.…”

Section: Time-reversible Dissipative Mapsmentioning

confidence: 99%

“…The simplest such map is a "reflection" about a mirror located at x = m [21]. For example, if we wished to map the regions (0 < x < m) and (rn < x < 1/2) into each other, we can define the reflection operation R, according to…”

Section: Time-reversible Dissipative Mapsmentioning

confidence: 99%

Microscopic Time-Reversibility and Macroscopic Irreversibility — Still a Paradox?

Posch

Dellago

Hoover

et al. 1997

Pioneering Ideas for the Physical and Chemical Sciences

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“…Here we show that a thermostated approach can be defined irrespective of boundary conditions, which, in the following, will be referred to by (A1)-(B). Even multibaker maps [9][10][11]13] can be generalized to mimic thermostating. They will be used to analytically work out expressions for the irreversible entropy production from the point of view of dynamical systems.…”

mentioning

confidence: 99%

“…(A1) In the thermostating algorithm a special force is introduced to avoid an uncontrolled growth of the kinetic energy of particles moving in external fields [2][3][4][5][6][7][8][9]. The force mimics the presence of a thermostat and makes the particle dynamics dissipative on average, although it preserves time reversibility.…”

mentioning

confidence: 99%

Equivalence of Irreversible Entropy Production in Driven Systems: An Elementary Chaotic Map Approach

1997

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A multibaker map is generalized in order to mimic the thermostating algorithm of transport models. Elementary calculations yield the irreversible entropy production caused by coarse graining of the phase-space density. For different systems, either in steady states (periodic or flux boundaries) or subjected to absorbing boundaries, the specific irreversible entropy production is shown to be u 2 ͞D, where u denotes the local streaming velocity (current per density) and D is the diffusion coefficient. [S0031-9007(97)04219-1] PACS numbers: 05.70.Ln, 05.45. + b, 51.10. + y The connection between nonequilibrium statistical physics and the underlying chaotic dynamics has become a subject of vivid interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The central questions are how the microscopic reversible dynamics can appear as an irreversible process on the macroscopic level, and how the macroscopic transport coefficients are related to microscopic characteristics of the chaotic dynamics. A careful analysis of the rate of irreversible entropy production is at the heart of this problem [16 -20], but the relation between complementary approaches has been poorly understood. Here, we present a consistent derivation of the irreversible entropy production for three main approaches to describe transport in driven systems producing currents. They model either nonequilibrium steady states (A) or the relaxation towards steady states (B):(A1) In the thermostating algorithm a special force is introduced to avoid an uncontrolled growth of the kinetic energy of particles moving in external fields [2][3][4][5][6][7][8][9]. The force mimics the presence of a thermostat and makes the particle dynamics dissipative on average, although it preserves time reversibility. The systems investigated up to now were assumed to be periodic of large spatial extension, and hence to be closed. The long time dynamics exhibits permanent chaos on an underlying chaotic attractor. Transport coefficients and the irreversible entropy production are connected with the average phase-space contraction rates ͑ p͒ on the attractor.(A2) By applying flux boundary conditions to an open Hamiltonian system it was shown that the steady-state density follows Fick's law [10], and the irreversible entropy production has been calculated [19]. In this case the current running through the system is due to the boundary condition only, and the phase-space contraction rate is zero,s ͑ f͒ 0.(B) The escape-rate formalism of transport processes is based on the investigation of open systems of large spatial extensions subjected to absorbing boundary conditions [11 -13]. In such cases the particle dynamics is chaotic in the sense of transient chaos, and there exists an underlying nonattracting chaotic set (a chaotic saddle) in the phase space. In the regime of linear response, at least, relaxation is closely related to steady-state transport. The transport coefficients of Hamiltonian systems are related [1,[11][12][13] to the chaotic saddle's escape rate k. In a recent ...

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Time-reversible dissipative ergodic maps

Cited by 33 publications

References 15 publications

Stochastic and dynamic properties of molecular dynamics systems: Simple liquids, plasma and electrolytes, polymers

Stochastic and dynamic properties of molecular dynamics systems: Simple liquids, plasma and electrolytes, polymers

Microscopic Time-Reversibility and Macroscopic Irreversibility — Still a Paradox?

Equivalence of Irreversible Entropy Production in Driven Systems: An Elementary Chaotic Map Approach

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