Thermodynamics and Statistics

  • Albrecht Lindner
  • Dieter Strauch
Part of the Undergraduate Lecture Notes in Physics book series (ULNP)


Classical thermodynamics can be derived from a set of axioms, but this chapter starts out from the statistical nature of quantum theory, thereby giving a meaning to these axioms. The binomial, Poisson, Gauss, and Maxwell distributions are compared with their implications for average values, correlations, and uncertainties. A basic issue is the minimum size of the phase space element. While classical differential equations are invariant under time reversal, the notion of entropy breaks this symmetry. We derive the relaxation-time approximation, the Liouville, collision-free Boltzmann, Langevin, and Fokker–Planck equations, and the fluctuation–dissipation theorem. The entropy theorem implies thermal, mechanical, and chemical equilibrium conditions using micro-canonical, canonical, grand-canonical, and other ensembles, with applications to gases, mixtures, Fermi gases, photons, and lattice vibrations. Phase transitions of first and second order and critical behavior in (real) gases, para- and ferromagnets, and also Bose–Einstein condensation are all reviewed. There is a list of 42 problems.

Supplementary material


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.PinnebergGermany
  2. 2.Theoretical PhysicsUniversity of RegensburgRegensburgGermany

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