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4 | 2008-2009
The Letter
Academic year 2008-2009
Selected papers
Inaugural lectures

Chair of Technological Innovation - Liliane Bettencourt

Academic Year 2008-2009
Mathias Fink
p. 19

Notes de la rédaction

Mathias Fink gave his inaugural lesson on 12 February 2009. His course entitled “Waves and images” began on 2 March 2009.

The inaugural lecture is available from Editions Fayard. The video is available on the College de France website.

Texte intégral

Extracts from the inaugural lecture:

1“I would like to show how a very fundamental research problem turned into a source of innovation. This research is situated at the interface of two main fields in physics: statistical thermodynamics, and waves. It is in statistical thermodynamics that the concepts of the inversion of time and reversibility are examined in the study of the behaviour of a large number of particles, whereas waves are generally studied in very different contexts: acoustics, electromagnetic fields, quantum mechanics, mathematics and engineering. Today I am going to talk about the transposition of particle thermodynamics to waves. The advantage of this thermodynamics is that the observer can become involved in the experience in a surprising way, for example to make a wave relive its past. […]

2One of the fundamental findings on which statistical thermodynamics is based, is that we live in an environment which seems irreversible: we see people around us ageing, not getting younger; a drop of colouring that falls into water diffuses, and we never see it reappear in its initial position. This apparent irreversibility of the macroscopic world has always intrigued physicists, as the equations of microscopic physics and mechanics are perfectly reversible.

3[…] To explain this tendency towards irreversibility, Ludwig Boltzmann introduced a concept of entropy which, in a sense, measures the disorder of a system of particles. He showed that, when we study a system of particles in interaction […] isolated from the rest of the universe, the natural tendency of all the particles is to evolve towards the greatest disorder; that is, towards maximal entropy. By introducing his famous H theorem, he was the first scientist to propose a microscopic explanation for the time arrow, but he had many critics […]. Some were very harsh: Poincaré pointed out that, if we waited for long enough, any isolated system would end up returning to its initial state. Other critics were more constructive, for instance his friend Loschmidt who proposed thought experiments involving little demons who, at time t, would be able to reverse the direction of the speed of every particle (without changing their size), which would enable a system to revert to its initial state. The debates were subsequently enhanced with the study of systems of unbalanced particles which can exchange particles and energy with the outside. This explained why, in certain conditions, the appearance of order was observed in these systems. This field has been explored in depth in recent decades, following the work of Ilya Prigogine. ‘The problem of interest to us here is not passively to observe the natural evolution of a system but, from an engineer’s point of view, to examine the possibility of creating a device that enables us to run experiments in both directions, from order to disorder and then, perfectly symmetrically, from disorder to order. What apparatus needs to surround our system of particles to be able to deliberately reverse the dynamics of these particles?’

4To solve this problem one first has to understand what is meant by the statement: microscopic physics is reversible. This statement is linked to the fundamental principle of dynamics, set forth by Newton, which states that a particle on which a force is exerted moves with an acceleration proportional to that force. It is the acceleration of the particle, that is, the second derived in relation to the time and position of the particle, that is proportional to the force, and it is the presence of this second derived that induces the reversibility of the laws of mechanics. Reversibility implies the following property when one observes the trajectories of two particles in interaction: if two highly skilled physicists (Loschmidt’s demons) were capable of stopping these two particles for an instant, after measuring their speed, and if later on they were capable of sending them back, at the same instant, by communicating to them opposing speeds, then these two particles would have no other possibility but to relive their pasts step by step, in other words, to cover their tracks in the opposite direction.”

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Référence papier

The Letter of the Collège de France, Collège de France, Paris, juin 2009, p. 19. ISSN 1958-1408

Référence électronique

Mathias Fink, « Chair of Technological Innovation - Liliane Bettencourt », La lettre du Collège de France [En ligne], 4 | 2008-2009, mis en ligne le 15 novembre 2010, consulté le 25 avril 2017. URL :

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Mathias Fink

Professor at the École supérieure de physique et de chimie industrielles de la ville de Paris, Director of the “Waves and Acoustics” Laboratory. Winner of the Louis Néel Grand Prix of the Société française de physique in 2008

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