Chapter 1
Introduction to Nonequilibrium
Statistical Physics and Its Foundations
Lamberto Rondoni
Abstract Statistical physics is a subject in which determinism and randomness,
probabilities and rigorous laws relating material properties of macroscopic objects
are finely intertwined. This calls for particular care in the interpretation of results.
When this is done, statistical physics, and in particular its nonequilbrium branch,
applies very widely to natural phenomena, but also to other fields, in which a statistical treatment is appropriate. In this paper, the fundamental elements and results of this
subject, meant to interpret the thermodynamic picture of matter in terms of the atomic
hypothesis, are reviewed. These include the Brownian motion; the Fluctutation Dissipation Theorem; the Boltzmann equation; the fluctuation relations; the linear and
the non-perturbative response theory. Furthemore, recent applications ranging from
active matter to the detection of gravitational waves and to machine learning are
briefly summarized. The literature cited in support of the text is supplemented by a
list of further readings, meant to fill some of the very many inevitable gaps in the
presentation of this subject.
Keywords Physical laws · Material properties · Determinism · Stochasticity ·
Probability · Emergence · Response to perturbations · Fluctuations
1.1 Prologue: The Realm of Theories and Measurements
Prepare a cup of Italian coffee, which means quite a small amount of hot water and
coffee. Lay it on a wooden table in a dining hall in a city, which is on Earth, which is
in the Solar system, in the Milky Way etc. Leave the cup on the table for a while; our
senses perceive that its temperature changes. In less than half an hour, we realize the
coffee has reached the room temperature. After a few days, the coffee is not there
L. Rondoni (B)
Dipartimento di Matematica, Politecnico di Torino,
corso Duca degli Abruzzi 24, 10129 Torino, Italy
e-mail: lamberto.rondoni@polito.it
Sezione di Torino, INFN, Via P. Giuria 1, 10125 Torino, Italy
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
X.-Y. Liu (ed.), Frontiers and Progress of Current Soft Matter Research,
Soft and Biological Matter, https://doi.org/10.1007/978-981-15-9297-3_1
1
Introduction to Nonequilibrium
Statistical Physics and Its Foundations
Lamberto Rondoni
Abstract Statistical physics is a subject in which determinism and randomness,
probabilities and rigorous laws relating material properties of macroscopic objects
are finely intertwined. This calls for particular care in the interpretation of results.
When this is done, statistical physics, and in particular its nonequilbrium branch,
applies very widely to natural phenomena, but also to other fields, in which a statistical treatment is appropriate. In this paper, the fundamental elements and results of this
subject, meant to interpret the thermodynamic picture of matter in terms of the atomic
hypothesis, are reviewed. These include the Brownian motion; the Fluctutation Dissipation Theorem; the Boltzmann equation; the fluctuation relations; the linear and
the non-perturbative response theory. Furthemore, recent applications ranging from
active matter to the detection of gravitational waves and to machine learning are
briefly summarized. The literature cited in support of the text is supplemented by a
list of further readings, meant to fill some of the very many inevitable gaps in the
presentation of this subject.
Keywords Physical laws · Material properties · Determinism · Stochasticity ·
Probability · Emergence · Response to perturbations · Fluctuations
1.1 Prologue: The Realm of Theories and Measurements
Prepare a cup of Italian coffee, which means quite a small amount of hot water and
coffee. Lay it on a wooden table in a dining hall in a city, which is on Earth, which is
in the Solar system, in the Milky Way etc. Leave the cup on the table for a while; our
senses perceive that its temperature changes. In less than half an hour, we realize the
coffee has reached the room temperature. After a few days, the coffee is not there
L. Rondoni (B)
Dipartimento di Matematica, Politecnico di Torino,
corso Duca degli Abruzzi 24, 10129 Torino, Italy
e-mail: lamberto.rondoni@polito.it
Sezione di Torino, INFN, Via P. Giuria 1, 10125 Torino, Italy
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
X.-Y. Liu (ed.), Frontiers and Progress of Current Soft Matter Research,
Soft and Biological Matter, https://doi.org/10.1007/978-981-15-9297-3_1
1