(Ir)reversibility and Entropy

Part of the Abel Symposia book series (ABEL, volume 7)


In the 1860’s emerges a revolutionary idea: many properties of the world around us can be explained by combining the atomistic hypothesis with the statistical theory. Some of the great scientific conquests from this time are the Boltzmann equation, which triggers one of the first qualitative studies of a complicated nonlinear partial differential equation; the notion of statistical entropy, which would later be fundamental in other areas of physics and mathematics, including information theory; and the notion of macroscopic irreversibility emerging from microscopically reversible laws. Thus the basic rules of statistical physics were set until Boltzmann’s irreversibility paradigm was shaken by Landau’s discovery of the Landau damping effect, about 80 years later, which opened the idea that equilibration is compatible with preservation of information, and led to a number of problems concerning the statistical theory of matter.


Boltzmann Equation Entropy Production Collision Operator Vlasov Equation Microscopic Dynamic 
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Authors and Affiliations

  1. 1.University of Lyon and Institut Henri PoincaréParis Cedex 05France

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