Statistical mechanics of stationary states. VI. Hydrodynamic fluctuation theory far from equilibrium

1980 ◽  
Vol 22 (2) ◽  
pp. 714-724 ◽  
Author(s):  
David Ronis ◽  
Itamar Procaccia ◽  
Jonathan Machta
Keyword(s):  
Statistical Mechanics ◽  
Fluctuation Theory ◽  
Stationary States ◽  
Far From Equilibrium ◽  
Hydrodynamic Fluctuation

Statistical mechanics of stationary states. V. Fluctuations in systems with shear flow

1980 ◽  
Vol 22 (6) ◽  
pp. 2809-2817 ◽  
Author(s):  
Jonathan Machta ◽  
Irwin Oppenheim ◽  
Itamar Procaccia
Keyword(s):  
Shear Flow ◽  
Statistical Mechanics ◽  
Stationary States

scholarly journals Universal biology and the statistical mechanics of early life

2017 ◽  
Vol 375 (2109) ◽  
pp. 20160341 ◽  
Author(s):  
Nigel Goldenfeld ◽  
Tommaso Biancalani ◽  
Farshid Jafarpour
Keyword(s):  
Statistical Mechanics ◽  
Genetic Code ◽  
Early Life ◽  
Minimal Models ◽  
Last Universal Common Ancestor ◽  
Universal Common Ancestor ◽  
Universal Biology ◽  
Fundamental Understanding ◽  
Far From Equilibrium ◽  
Dynamical System Models

All known life on the Earth exhibits at least two non-trivial common features: the canonical genetic code and biological homochirality, both of which emerged prior to the Last Universal Common Ancestor state. This article describes recent efforts to provide a narrative of this epoch using tools from statistical mechanics. During the emergence of self-replicating life far from equilibrium in a period of chemical evolution, minimal models of autocatalysis show that homochirality would have necessarily co-evolved along with the efficiency of early-life self-replicators. Dynamical system models of the evolution of the genetic code must explain its universality and its highly refined error-minimization properties. These have both been accounted for in a scenario where life arose from a collective, networked phase where there was no notion of species and perhaps even individuality itself. We show how this phase ultimately terminated during an event sometimes known as the Darwinian transition, leading to the present epoch of tree-like vertical descent of organismal lineages. These examples illustrate concrete examples of universal biology: the quest for a fundamental understanding of the basic properties of living systems, independent of precise instantiation in chemistry or other media. This article is part of the themed issue ‘Reconceptualizing the origins of life’.

ON THE EXTENSIVITY OF THE ENTROPY Sq FOR N ≤ 3 SPECIALLY CORRELATED BINARY SUBSYSTEMS

2006 ◽  
Vol 16 (06) ◽  
pp. 1727-1738 ◽  
Author(s):  
YUZURU SATO ◽  
CONSTANTINO TSALLIS
Keyword(s):  
Statistical Mechanics ◽  
Stationary States ◽  
Nonextensive Statistical Mechanics ◽  
Entropy Formula ◽  
Gibbs Entropy ◽  
Statistical Mechanical

Many natural and artificial systems whose range of interaction is long enough are known to exhibit (quasi)stationary states that defy the standard, Boltzmann–Gibbs statistical mechanical prescriptions. For handling such anomalous systems (or at least some classes of them), nonextensive statistical mechanics has been proposed based on the entropy [Formula: see text], with [Formula: see text] (Boltzmann–Gibbs entropy). Special collective correlations can be mathematically constructed such that the strictly additive entropy is now Sq for an adequate value of q ≠ 1, whereas Boltzmann–Gibbs entropy is nonadditive. Since important classes of systems exist for which the strict additivity of Boltzmann–Gibbs entropy is replaced by asymptotic additivity (i.e. extensivity), a variety of classes are expected to exist for which the strict additivity of Sq (q ≠ 1) is similarly replaced by asymptotic additivity (i.e. extensivity). All probabilistically well defined systems whose adequate entropy is S1 are called extensive (or normal). They correspond to a number W eff of effectively occupied states which grows exponentially with the number N of elements (or subsystems). Those whose adequate entropy is Sq (q ≠ 1) are currently called nonextensive (or anomalous). They correspond to W eff growing like a power of N. To illustrate this scenario, recently addressed [Tsallis, 2004] we provide in this paper details about systems composed by N = 2, 3 two-state subsystems.

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