Entropy balance, time reversibility, and mass transport in dynamical systems

Wolfgang Breymann, T. Tél, Jürgen Vollmer

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

We review recent results concerning entropy balance in low-dimensional dynamical systems modeling mass (or charge) transport. The key ingredient for understanding entropy balance is the coarse graining of the local phase-space density. It mimics the fact that ever refining phase-space structures caused by chaotic dynamics can only be detected up to a finite resolution. In addition, we derive a new relation for the rate of irreversible entropy production in steady states of dynamical systems: It is proportional to the average growth rate of the local phase-space density. Previous results for the entropy production in steady states of thermostated systems without density gradients and of Hamiltonian systems with density gradients are recovered. As an extension we derive the entropy balance of dissipative systems with density gradients valid at any instant of time, not only in stationary states. We also find a condition for consistency with thermodynamics. A generalized multi-Baker map is used as an illustrative example.

Original languageEnglish
Pages (from-to)396-408
Number of pages13
JournalChaos
Volume8
Issue number2
Publication statusPublished - Jun 1998

Fingerprint

Time Reversibility
Mass Transport
dynamical systems
Dynamical systems
Entropy
Mass transfer
Dynamical system
entropy
Phase Space
space density
Entropy Production
Gradient
gradients
Hamiltonians
Charge Transport
Coarse-graining
Dissipative Systems
refining
Chaotic Dynamics
Stationary States

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Entropy balance, time reversibility, and mass transport in dynamical systems. / Breymann, Wolfgang; Tél, T.; Vollmer, Jürgen.

In: Chaos, Vol. 8, No. 2, 06.1998, p. 396-408.

Research output: Contribution to journalArticle

Breymann, W, Tél, T & Vollmer, J 1998, 'Entropy balance, time reversibility, and mass transport in dynamical systems', Chaos, vol. 8, no. 2, pp. 396-408.
Breymann, Wolfgang ; Tél, T. ; Vollmer, Jürgen. / Entropy balance, time reversibility, and mass transport in dynamical systems. In: Chaos. 1998 ; Vol. 8, No. 2. pp. 396-408.
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