Ludwig Boltzmann Forum

Gerhard Fasol: Entropy, information and Ludwig Boltzmann

Entropy, information and Ludwig Boltzmann, 10th Ludwig Boltzmann Forum 20 February 2018

Gerhard Fasol CEO, Eurotechnology Japan KK, Board Director, GMO Cloud KK. former faculty Cambridge University and past Fellow, Trinity College Cambridge

Ludwig Boltzmann 20 February 1844 – 5 September 1906

Ludwig Boltzmann 20 February 1844 - 5 September 1906
Ludwig Boltzmann 20 February 1844 – 5 September 1906

We use Ludwig Boltzmann’s results every day. Here are some examples:

  • The definition of the units of temperature, Kelvin, Celsius, are directly linked to Boltzmann’s constant
  • The Stefan-Boltzmann radiation law tells us that the total energy emitted by a black body per unit surface area is proportional to the 4th power of the temperature, and allows us to measure temperatures at a distance. For example, the temperature of the surface of the sun can be measured using the Stefan-Boltzmann radiation law
  • Boltzmann’s formula S = k log W links the macroscopic Entropy with the probability (W = Wahrscheinlichkeit) of a macrostate
  • Boltzmann’s transport equations are used for many purposes, to simulate carrier transport in semiconductor devices, and to design airplanes, turbine blades and cars
  • Ludwig Boltzmann’s philosophy of nature contributes to our understanding of nature and our world

Ludwig Boltzmann was proposed several times for the Nobel Prize: 1903, 1905 and three times in 1906, the year he took his life in Duino, Italy.

Ludwig Boltzmann achieved his Matura, Austria’s high-school examination required to enter University education at the age of 19 in 1863.

In 1865, at the age of 21, he published his first research paper entitled “Über die Bewegung der Elektrizität in krummen Flächen” (electricity in curved surfaces). It was the dawn of our electrical age, Maxwell created his Maxwell’s equations in 1861-1862, and on 15 February 1883, 20 years later, Tokyo Dentsu KK received the license to start its electricity business in Tokyo.

Among Ludwig Boltzmann’s teachers were Josef Loschmidt and Jozef Stefan.

Josef Loschmidt proposed structures for 300 chemical compounds including benzene, he determined the number of gas molecules in a given volume and the Loschmidt constant is named after him.

Jozef Stefan created the Stefan-Boltzmann Law with Ludwig Boltzmann, and used it to determine the temperature of the surface of the sun.

Ludwig Boltzmann traveled extensively, was in correspondence and discussions and scientific exchange with most major scientists of the time. He also moved professionally:

  • University of Vienna
  • 1867-1869 Privat-Dozent
  • 1869-1873 Full Professor of Mathematical Physics in Graz
  • 1873-1876 Full Professor of Mathematics in Vienna
  • 1876-1890 Full Professor at University of Graz, Head of the Institute of Physics
  • 1887-1888 Rektor (President) of the University of Graz
  • 1890-1894 Professor University of München
  • 1894-1900 Professor University of Vienna
  • 1900-1902 Professor of Theoretical Physics University of Leipzig
  • 1902- Professor University of Vienna

Ludwig Boltzmann supported and worked with women:

One of Ludwig Boltzmann’s students was Lise Meitner (November 1878 – 27 October 1968). Lise Meitner was part of Otto Han’s team that discovered nuclear fission, Otto Hahn was awarded the Nobel Prize. Lise Meitner was the second woman to earn a PhD degree in Physics at the University of Vienna. The Element 109, Meitnerium is named about Lise Meitner.

The first President of Osaka University (1931-1934), Nagaoka Kantaro (1865 – 1950) was Ludwig Boltzmann’s student in München around 1892-1893.

The unit of temperature, Celsius or Kelvin, is directly linked to Boltzmann’s constant k

Currently the unit of Temperature Kelvin is defined as follows:

One Kelvin is defined such that the temperature of the triple point of water is exactly 273.16 Kelvin.
For this definition to be reproducible, the water needs to be defined: its defined as VSNOW = Vienna Standard Mean Ocean Water.
While this definition may have been best at the time it was set, clearly its not sufficient for today.

When the SI system of physical units will be redefined next year, the definition of the unit of temperature, Kelvin will be:

Kelvin is defined such, that the numerical value of the Boltzmann constant k is equal to exactly 1.380650 x 10^-23 JK^-1.

Thus the unit of temperature Kelvin is directly linked to Boltzmann’s constant.

For more details, see: Boltzmann constant and the new SI system of units

What is Entropy?

Entropy measures information, entropy is the measure of information.

Macro-states, determined for example by the macroscopic quantities pressure (p), Volume (V), or Temperature (T), or number of particles (N), contain a very large number of micro-states.

Boltzmann’s Entropy S = k logarithm of the phase volume(= the probability) of a macro-state in terms of the possible micro-states.

Different faces of Entropy

Entropy has many faces

  • thermodynamic entropy, is a macroscopic state parameter of a system in equilibrium, like temperature, pressure, volume. However, can we measure entropy directly?
  • microscopic, statistical entropy
    • Boltzmann Entropy: S = k log W
    • Gibbs entropy
  • information theory
    • Shannon’s entropy

Shannon’s entropy

Shannon: “I thought of calling it “information”. But the word was overly used, so I decided to call it “uncertainty”. When I discussed it with John von Neumann, he had a better idea:

  1. in the first place your uncertainty has been used in statistical mechanics (ie by Boltzmann) under that name, so it already has a name
  2. in the second place, and more importantly, no one knows what entropy really is, so in a debate you will always have the advantage

What can we learn from Ludwig Boltzmann?

  • Empower young people, recognize and support talent early
    • LB published first scientific work at age 21
    • Full Professor at 25
    • Head of Department at 32
    • President of University at 43
  • Talent is not linear – talent is exponential
  • Move around the world. Connect. Interact.
  • Empower women (LB promoted many women)
  • Don’t accept authority for authority’s sake
  • Science/physics issues need to be treated with the methods of physics/science
  • No dogmas
  • Support entrepreneurs (LB supported airplane developers before airplanes existed)
10th Ludwig Boltzmann Forum 2018, Tuesday 20 February 2018 at the Embassy of Austria in Tokyo
10th Ludwig Boltzmann Forum 2018, Tuesday 20 February 2018 at the Embassy of Austria in Tokyo
10th Ludwig Boltzmann Forum 2018, Tuesday 20 February 2018 at the Embassy of Austria in Tokyo
10th Ludwig Boltzmann Forum 2018, Tuesday 20 February 2018 at the Embassy of Austria in Tokyo

Copyright (c) 2018 Eurotechnology Japan KK All Rights Reserved

leadership Ludwig Boltzmann Symposium

Gerhard Fasol: Ludwig Boltzmann – Energy, Entropy Leadership by

Ludwig Boltzmann as leader

Gerhard Fasol

Keynote presented at the 6th Ludwig Boltzmann Symposium on February 20, 2014 at the Embassy of Austria in Tokyo.

Ludwig Boltzmann created much of the basic fundament of today's physics. Ludwig Boltzmann also was an outstanding leader. Talk by Gerhard Fasol.
Ludwig Boltzmann created much of the basic fundament of today’s physics. Ludwig Boltzmann also was an outstanding leader. Talk by Gerhard Fasol.

(Gerhard Fasol, CEO of Eurotechnology Japan KK. Served as Associate Professor of Tokyo University, Lecturer at Cambridge University, and Manger of Hitachi Cambridge R&D Lab.)

Ludwig Boltzmann, the scientist

Ludwig Boltzmann’s greatest contribution to science is that he linked the macroscopic definition of Entropy which came from optimizing steam engines at the source of the first industrial revolution to the microscopic motion of atoms or molecules in gases, this achievement is summarized by the equation S = k log W, linking entropy S with the probability W. k is the Boltzmann constant, one of the most important constants in nature, linked directly to temperature in the SI system of physical units. This monumental work is maybe Boltzmann’s most important creation but by far not the only one. He discovered many laws, and created many mathematical tools, for example Boltzmann’s Equations, which are used today as tools for numerical simulations of gas flow for the construction of jet engines, airplanes, automobiles, in semiconductor physics, information technology and many other areas. Although independently discovered, Shannon’s theory of noise in communication networks, and Shannon’s entropy in IT is also directly related to Boltzmann’s entropy work.

Ludwig Boltzmann, the leader

Ludwig Boltzmann was not only a monumental scientist, but also an exceptional leader, teacher, educator and promoter of exceptional talent, and he promoted many women.

One of the women Ludwig Boltzmann promoted was Henriette von Aigentler, who was refused permission to unofficially audit lectures at Graz University. Ludwig Boltzmann advised and helped her to appeal this decision, in 1874, Henriette von Aigentler passed her exams as a high-school teacher, and on July 17, 1876, Ludwig Boltzmann married Henriette von Aigentler, my great-grand mother.

Another woman Ludwig Boltzmann promoted was his student Lise Meitner (Nov 1878 – Oct 27, 1968), who later was part of the team that discovered nuclear fission, work for which Otto Hahn was awarded the Nobel Prize. Lise Meitner was also the second woman to earn a Doctorate degree in Physics from the University of Vienna. Element 109, Meitnerium, is named after Lise Meitner.

Nagaoka Hantaro, First President of the University of Osaka – Ludwig Boltzmann’s pupil

The first President of Osaka University (1931-1934), Nagaoka Hantaro (1865 – 1950) was Ludwig Boltzmann’s pupil around 1892 – 1893 at Muenchen University.

Ludwig Boltzmann, a leader of science

Ludwig Boltzmann was connected in intense discussions with all major scientists of his time, he travelled extensively including three trips to the USA in 1899, 1904 and 1905, about which he wrote the article “Die Reise eines deutschen Professors ins El Dorado”, published in the book “Populäre Schriften”.

Ludwig Boltzmann published his first scientific publication at the age of 21 years in 1865. He was appointed Full Professor of Mathematical Physics at the University of Graz in 1869 at the age of 25 years, later in 1887-1888 he was Rektor (President) of the University of Graz at the age of 43 years.

He spent periods of his professional work in Vienna, at Graz University (1869-1873 and 1876-1890), at Muenchen University (1890-1894). When working at Muenchen University, he discovered that neither he nor his family would not receive any pension from his employment at Muenchen University after an eventual retirement or in case he dies before retirement, and therefore decided to return to Vienna University in 1894, where he and his family were assured of an appropriate pension. During 1900-1902 he spent two years working in Leipzig, where he cooperated with the Nobel Prize winner Friedrich Wilhelm Ostwald.

Ludwig Boltzmann did not shy away from forceful arguments to argue for his thoughts and conclusions, even if his conclusions were opposite to the views of established colleagues, or when he felt that philosophers intruded into the field of physics, i.e. used methods of philosophy to attempt solving questions which needed to be solved with physics measurements, e.g. to determine whether our space is curved or not. Later in his life he was therefore also appointed to a parallel Chair in Philosophy of Science, and Ludwig Boltzmann’s work in Philosophy of Science is also very fundamentally important.

I discovered the unpublished manuscripts of Boltzmann’s lectures on the Philosophy of Science, stimulated and encouraged by myself, and with painstaking work my mother transcribed these and other unpublished manuscripts, and prepared them for publication, to make these works finally accessible to the world, many years after Ludwig Boltzmann’s death.

Ludwig Boltzmann was a down to earth man. He rejected the offer of Nobility by His Majesty, The Emperor of Austria, i.e. the privilege to be named Ludwig von Boltzmann (or a higher title) instead of commoner Ludwig Boltzmann. Ludwig Boltzmann said: “if our common name was good enough for my parents and ancestors, it will be good enough for my children and grand children…”

Summary: understanding Ludwig Boltzmann.

Boltzmann’s thoughts and ideas are a big part of our understanding of the world and the universe.

His mathematical tools are used every day by today’s engineers, bankers, IT people, physicists, chemists… and even may contribute to solve the world’s energy problems.

Ludwig Boltzmann stood up for his ideas and conclusions and did not give in to authority. He rejected authority for authority’s sake, and strongly pushed his convictions forward.

What can we learn from Ludwig Boltzmann?

  • empower young people, recognize and support talent early.
  • exceptional talent is not linear but exponential.
  • move around the world. Connect. Interact.
  • empower women.
  • don’t accept authority for authority’s sake.
  • science/physics/nature need to be treated with the methods of physics/science.
  • no dogmas.
  • support entrepreneurs, Ludwig Boltzmann did.
Gerhard Fasol
Gerhard Fasol

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