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

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

doi:10.1007/978-1-4899-0268-9_24

Cited by 5 publications

(3 citation statements)

References 26 publications

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“…This subject has generated many profound questions and techniques whose relevance goes beyond statistical physics. For example, the transition between the molecular dynamics and the human (thermodynamic) length scales is still investigated [4,9,45] and gives rise to the notion of statistical entropy, which has proved to be a fundamental tool in many areas of modern sciences [16,20,24].…”

Section: Introductionmentioning

confidence: 99%

Tropical limit and a micro-macro correspondence in statistical physics

Angelelli¹

2017

J. Phys. A: Math. Theor.

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Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituent (elements) that is well-behaved with respect to composition. This kind of connection is studied with maps that preserve a monoid structure. The approach highlights an underlying order relation that is explored through the concepts of filter and ideal. Main attention is paid to asymmetry and duality between max-and min-criteria. Physical implementations are presented through simple examples in thermodynamics and non-equilibrium physics. The phenomenon of ultrametricity, the notion of tropical equilibrium and the role of ground energy in non-equilibrium models are discussed. Tropical symmetry, i.e. idempotence, is investigated.

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Section: Introductionmentioning

confidence: 99%

Tropical limit and a micro-macro correspondence in statistical physics

Angelelli¹

2017

J. Phys. A: Math. Theor.

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“…I expected that an analog of their shear-stress fluctuations could be found in the qualitatively simpler dynamics of a nonequilibrium Baker Map. [2][3][4] The simplicity of the map provides a worthwhile pedagogical approach to understanding the Evans-Cohen-Morriss "Fluctuation Theorem". The "Theorem" is not quite an identitity.…”

Section: Introductionmentioning

confidence: 99%

“…If we associate the logarithm of phase-space area with Gibbs' entropy the entropy changes by ±k ln(2) with each iteration of the map. Because the region subject to halving is twice as large as that subject to doubling, the net effect is an entropy decrease averaging −(k/3) ln (2) per iteration. Let us apply some steady-state thermodynamics.…”

Section: Introductionmentioning

confidence: 99%