*Olivier Darrigol*

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198816171
- eISBN:
- 9780191853661
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198816171.003.0010
- Subject:
- Physics, Atomic, Laser, and Optical Physics, History of Physics

In this last chapter, the reader will find synthetic reflections on Boltzmann’s sources, on the basic components of his theory, and on the ways it was received. The basic components are arranged ...
More

In this last chapter, the reader will find synthetic reflections on Boltzmann’s sources, on the basic components of his theory, and on the ways it was received. The basic components are arranged according to the natural order in which they occurred in Boltzmann’s theory making: constructive tools, chief constructions, crucial predictions, underlying concepts, bridges between different approaches. To fully understand his enterprise, one must embrace his theory as an entire whole organism. This is a difficult and time-consuming task, which this book is meant to ease. In the past, Boltzmann’s readers fortunately did not need a historian’s thoroughness in order to benefit from his multiple constructs and insights. These elements, even taken out of context, had enough power to propel diverging theoretical projects from Boltzmann’s times to ours. In many ways, Boltzmann’s theory anticipated the richness, diversity, and residual opacity of modern statistical mechanics.Less

In this last chapter, the reader will find synthetic reflections on Boltzmann’s sources, on the basic components of his theory, and on the ways it was received. The basic components are arranged according to the natural order in which they occurred in Boltzmann’s theory making: constructive tools, chief constructions, crucial predictions, underlying concepts, bridges between different approaches. To fully understand his enterprise, one must embrace his theory as an entire whole organism. This is a difficult and time-consuming task, which this book is meant to ease. In the past, Boltzmann’s readers fortunately did not need a historian’s thoroughness in order to benefit from his multiple constructs and insights. These elements, even taken out of context, had enough power to propel diverging theoretical projects from Boltzmann’s times to ours. In many ways, Boltzmann’s theory anticipated the richness, diversity, and residual opacity of modern statistical mechanics.

*Olivier Darrigol*

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198816171
- eISBN:
- 9780191853661
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198816171.003.0006
- Subject:
- Physics, Atomic, Laser, and Optical Physics, History of Physics

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to ...
More

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.Less

This chapter recounts how Boltzmann reacted to Hermann Helmholtz’s analogy between thermodynamic systems and a special kind of mechanical system (the “monocyclic systems”) by grouping all attempts to relate thermodynamics to mechanics, including the kinetic-molecular analogy, into a family of partial analogies all derivable from what we would now call a microcanonical ensemble. At that time, Boltzmann regarded ensemble-based statistical mechanics as the royal road to the laws of thermal equilibrium (as we now do). In the same period, he returned to the Boltzmann equation and the H theorem in reply to Peter Guthrie Tait’s attack on the equipartition theorem. He also made a non-technical survey of the second law of thermodynamics seen as a law of probability increase.

*Olivier Darrigol*

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198816171
- eISBN:
- 9780191853661
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198816171.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics, History of Physics

This chapter is the first subset of a set of critical summaries Boltzmann’s writings on kinetic-molecular theory. It covers a first period in which he tried to construct the laws of thermal ...
More

This chapter is the first subset of a set of critical summaries Boltzmann’s writings on kinetic-molecular theory. It covers a first period in which he tried to construct the laws of thermal equilibrium, including the existence of the entropy function and the Maxwell–Boltzmann law, by various means including the principle of least action, Maxwell’s collision formula, the ergodic hypothesis, and a procedure of adiabatic variation. This is an immensely fertile period in which Boltzmann introduced several of the basic concepts, problems, and difficulties of modern statistical mechanics.Less

This chapter is the first subset of a set of critical summaries Boltzmann’s writings on kinetic-molecular theory. It covers a first period in which he tried to construct the laws of thermal equilibrium, including the existence of the entropy function and the Maxwell–Boltzmann law, by various means including the principle of least action, Maxwell’s collision formula, the ergodic hypothesis, and a procedure of adiabatic variation. This is an immensely fertile period in which Boltzmann introduced several of the basic concepts, problems, and difficulties of modern statistical mechanics.