Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium

Connections between microscopic dynamical observables and macroscopic nonequilibrium (NE) properties have been pursued in statistical physics since Boltzmann, Gibbs, and Maxwell. The simulations we describe here establish a relationship between the Kolmogorov–Sinai entropy and the energy dissipated...

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Published inProceedings of the National Academy of Sciences - PNAS Vol. 110; no. 41; pp. 16339 - 16343
Main Authors Green, Jason R., Costa, Anthony B., Grzybowski, Bartosz A., Szleifer, Igal
Format Journal Article
LanguageEnglish
Published United States National Academy of Sciences 08.10.2013
NATIONAL ACADEMY OF SCIENCES
National Acad Sciences
Subjects
Computer Simulation
Energy dissipation
Entropy
Hot Temperature
Mathematical vectors
Models, Theoretical
Nanostructures
Particle energy
Particle interactions
Particle trajectories
Physical Sciences
Physics
Self assembly
Statistical mechanics
Tangents
Thermodynamic equilibrium
Thermodynamics
Trajectories
nonequilibrium self-assembly
Lyapunov exponents
dynamic entropy
statistical mechanics
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Summary:Connections between microscopic dynamical observables and macroscopic nonequilibrium (NE) properties have been pursued in statistical physics since Boltzmann, Gibbs, and Maxwell. The simulations we describe here establish a relationship between the Kolmogorov–Sinai entropy and the energy dissipated as heat from a NE system to its environment. First, we show that the Kolmogorov–Sinai or dynamical entropy can be separated into system and bath components and that the entropy of the system [Formula] characterizes the dynamics of energy dissipation. Second, we find that the average change in the system dynamical entropy is linearly related to the average change in the energy dissipated to the bath. The constant energy and time scales of the bath fix the dynamical relationship between these two quantities. These results provide a link between microscopic dynamical variables and the macroscopic energetics of NE processes.
Bibliography:http://dx.doi.org/10.1073/pnas.1312165110
Edited† by R. Stephen Berry, The University of Chicago, Chicago, IL, and approved August 29, 2013 (received for review June 26, 2013)
Author contributions: J.R.G., A.B.C., B.A.G., and I.S. designed research; J.R.G. and A.B.C. performed research; J.R.G., A.B.C., and I.S. analyzed data; and J.R.G., A.B.C., B.A.G., and I.S. wrote the paper.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1312165110