# nLab thermodynamics

## Surveys, textbooks and lecture notes

#### Measure and probability theory

measure theory

probability theory

# Contents

## Idea

It is practically impossible to model a macroscopic system in terms of the microscopic kinematical and dynamical variables of all its particles. Thus one makes a hierarchical reduction in which this complexity is reduced to small number of collective variables. The theoretical framework for such reductions for systems is statistical mechanics or statistical physics.

One special case of hierarchical reduction is the limit of large volumes $V$, in which the number of particles (of each species) per volume, $N/V$, stays constant. This is called the thermodynamic limit in statistical physics. Under some standard assumptions like homogeneity (spacial and possibly directional) and stability (no transitory effects), there is a small number of collective variables characterizing the system. Such a description can be (and historically was) postulated as an independent self-consistent phenomenological theory even without going into the details of statistical mechanics; such a description is called equilibrium thermodynamics, which is believed to be deducible from statistical mechanics, as has been partially proved for some classes of systems. Sometimes transitional finite-time phenomena are described either statistically by studying stochastic processes or by a more elaborate hierarchical form of thermodynamics, so-called nonequilibrium thermodynamics.

One of the basic characteristics of a thermodynamical system is its temperature, which has no analogue in fundamental non-statistical physics. Other common thermodynamical variables include pressure, volume, entropy, enthalpy etc.

## References

### General

A formalization in terms of symplectic geometry is in chapter IV “Statistical mechanics” of

• Jean-Marie Souriau, Structure of dynamical systems. Asymplectic view of physics . Translated from the French by C. H. Cushman-de Vries. Translation edited and with a preface by R. H. Cushman and G. M. Tuynman. Progress in Mathematics, 149. Birkhäuser Boston, Inc., Boston, MA, 1997

as well as in

• Azimuth Project, Thermodynamics

• A. Bravetti, C. S. Lopez-Monsalvo, F. Nettel, Contact symmetries and Hamiltonian thermodynamics, arxiv/1409.7340

For an thorough introduction to common misconceptions at an elementary level:

• John Denker. Modern Thermodynamics. web, pdf.

A survey of irreversible thermodynamics is in

• Ivan Vavruch, Conceptual problems of modern irreversible thermodynamics, Chem. Listy 96 (2002) (pdf)