# Statistical Physics

## A Prelude and Fugue for Engineers

** Gradus ad Parnassum in Statistical Physics **

The first lesson of this textbook is the dedication at page iv “to all my students, who taught me the difficult art of teaching”. I’m grateful to Roberto for adding in pencil my name below that line of my book copy, as I consider myself one of those students after learning so much from this book. I fully share the concept expressed in the dedication, which actually reflects the substance and the style of the book. Gaining new knowledge is a rewarding joint endeavour, and the logical clarification process which makes knowledge understandable to newcomers is an essential step of its transmission. Such clarification rests on the historical sequence of notions and the links, either instrumental or analogical, among different disciplines. In this way an interactive teaching may become an effective part of research.

The parallel with musical forms, providing
the appropriate tune to the book and its
chapters, recalls another basic aspect of
science, the fundamental role of creativity and
intuition on one side, and the essential need
to be expressed in a rigorous language on
the other side. It is implicit that the beauty of
music and that of science have comparable
aesthetic values: *Scientia reddit opus pulchrum*,
wrote Bonaventure. Considering the original
destination of the book to engineers, one may
think of this statement as addressing to applied
science, but the Preface admonishes the
readers with Pasteur’s words that there is no
applied science, but only science applications.

Far-reaching applications always start from a solid background in basic science and a curiosity-driven crossdisciplinary attitude. Due to present rapid increase of knowledge and technology, no student can hope today to learn in the class exactly what will be requested at the end of his studies. That’s why high schools and university should first of all stimulate curiosity and open the mind of their students, more than just teaching a profession.

Another concept inspiring the author is
that a valuable textbook should remain a
good companion all along the professional
career. This is here achieved with three levels
of learning aids: the *basic requirements*,
including also notions currently not included
in engineer curricula such as the elementary
concepts of quantum mechanics, etc.; the *focus
on applications*, in harmony with the author’s
statement that *scientists aim to understand the
world, engineers to change it*. The third level
is *graded learning*: the book is organized in
closely connected sections, which according
to their marks (stars and playing-card suits) are
suitable to the undergraduate, as well as to the
graduate, and doc/post-doc levels: something
worth being kept in the bookshelf for ever,
and possibly integrated by the numerous
additional readings suggested at the end of
each chapter.

As we rapidly go through this symphony, we
are first requested in Chapter 1 to play by ear
the basic notions of classical thermodynamics:
time and temperature, work, energy, entropy,
thermodynamic potentials, up to the Brownian
motion, casting our eyes into the microworld.
This in introduced in Chapter 2 with the
ouverture in B major, *i.e.*, the
statistical approach, from the thermodynamics
of ideal gases to the Gibbs paradox and
Maxwell-Boltzmann approximation. By
comparing the worlds of Newton’s apples and
Schrödinger’s cats and that of distinguishable
and undistinguishable particles, quantum
mechanics knocks on the door. It is opened
at Chapter 3, accompanied by “easy rhytms
and melodies”: after a thorough discussion
of *canonical* distributions, the specific heat of
solids and the low-temperature enigma come
about, solved by his majesty h-bar. The work
by Petit et Dulong and the corresponding
law, dating back to as early as 1819, offers the
occasion for a masterful *intermezzo*, a pièce of
history of physics illustrating “the bright and
dark sides of experimental science”. Together
with the elementary, clear introduction
to the dynamics of solids, the frequent
reference to magnetic systems and models
is quite appropriate on both the tutorial and
applicative levels.

Chapter 4 on *fluid chords* moves to the
statistical physics of real gases and charged
fluids, “from plasmas to DNA”, and to a
precious (starred) section on the microscopic
structure of liquids. It is indeed a *crescendo*
the one which takes us to Chapter 5 on
ferromagnetism, spontaneous symmetry
breaking and the role of fluctuations, up to
scaling and renormalization (the latter with
their obvious stars). With the stat-physics
of open systems and grand-canonical
distributions we enter the vast world of
inhomogeneous systems and gas-surface
interactions (Chapter 6), but the growing
importance in condensed matter of electrons
and related optical properties, where energies
largely exceed the experimental temperature,
imposes low-temperature physics, *i.e.*,
quantum mechanics and quantum statistics.

Chapter 7 on “fuzzy and cool melodies” introduces the reader to fermions and bosons, overviewing the basic facts on which rests quantum statistical physics, say Planck’s theory of the black-body spectrum, the theory of free electrons in metals, Bose-Einstein condensation and superfluidity, and, for refined listeners in search of stars, superfluid helium-3. All these extraordinary variations on the theme are closed by the canonical fugue.

The book is enriched by five appendices, A to
E. A presents the mathematical tools necessary
to a deeper understanding of statistical physics.
B, quoting “the rest is noise” –a famous book
by Axel Ross on XX century music– actually
speaks of entropy and information, which in
nonlinear thermodynamics could even lead
to music (order) out of noise (chaos). C offers
a substantial historical section illustrating the
roots of fundamental concepts in statistical
mechanics. Random walks, diffusion and the
Langevin equation, the scattering of identical
particles and the rules of detailed balance
are summarized in D and E, the last notes of
this excellent score. The colloquial style of the
entire book, full of wit and humour, shows how
one of the most exciting and important parts
of physics can be conveyed (played) in the form
of a *divertimento*, without being less rigorous
and thorough than needed: a lesson for smart
students and young professors training in the
difficult art of teaching.

Giorgio Benedek

Università Milano-Bicocca

- Roberto Piazza
- Statistical Physics
- A Prelude and Fugue for Engineers

- UNITEXT for Physics. Springer Nature, 2017
- hardcover: pp. XV + 453, € 72,79
- ISBN: 978-3-319-44536-6
- e-book: € 59,49
- ISBN: 978-3-319-44537-3