Statistical Mechanics: Entropy, Order Parameters, and Complexity

By James P. Sethna. 2021

310 citations recorded by the source corpus.

This text distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, active matter, and dynamical systems. Chapters address random walks, equilibrium systems, entropy, free energies, quantum systems, calculation and computation, order parameters and topological defects, correlations and linear response theory, and abrupt and continuous phase transitions. Exercises explore the enormous range of phenomena where statistical mechanics provides essential insight — from card shuffling to how cells avoid errors when copying DNA, from the arrow of time to animal flocking behavior, from the onset of chaos to fingerprints. The text is aimed at graduates, undergraduates, and researchers in mathematics, computer science, engineering, biology, and the social sciences as well as to physicists, chemists, and astrophysicists. As such, it focuses on those issues common to all of these fields, background in quantum mechanics, thermodynamics, and advanced physics should not be needed, although scientific sophistication and interest will be important.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f875601a7abf40e8bccd8494ea4bd14d6ca24729

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In Statistical and Nonlinear Physics

Citations in the corpus

Python for Education: Computational Methods for Nonlinear Systems (2007, methodology): “rates, (2) getting an exponentially distributed random time from rates, (3) choosing a random reaction with probability proportional to reaction rate, (4) executing the chosen reaction based on its stoichiometry, and (5) returning the time at which the reaction takes place””” # ( 1 ) self.GetReactio”
Colloquium: Criticality and dynamical scaling in living systems (2017, background): “3 See, e.g. Binney et al. (1993); De Gennes (1979); Delamotte (2012); Henkel et al. (2008); Sethna (2006); Stanley (1987); Täuber (2017). resolution (Sejnowski et al., 2014)– and, similarly, in genomics (Lesk, 2017) or in collective motion analyses (Cavagna et al., 2008).”
Theoretical perspective on the glass transition and amorphous materials (2010, background): “…textbook on liquids (Hansen and McDonald, 2006), while statistical mechanics textbooks usually culminate with a presentation of our current understanding of phase transitions in pure materials using renormalization group concepts (Chandler, 1987; Sethna, 2006), leaving out disordered systems.”
Random walks and diffusion on networks (2016, background): “pT ij= p j T ji: (32) In other words, for each edge, the ow of probability in each direction must equal each other at equilibrium. This property, called \detailed balance" in statistical physics [116] and \time reversibility" in mathematics [1, 42], does not generally hold for directed net”