A Royal Road to Topology

10.1142/12154 ◽  
2021 ◽  
Author(s):  
Szymon Dolecki
Keyword(s):  
Royal Road

The Analogical Turn (1884–1887)

2018 ◽  
Author(s):  
Olivier Darrigol
Keyword(s):  
Boltzmann Equation ◽  
Statistical Mechanics ◽  
Mechanical System ◽  
Thermal Equilibrium ◽  
Special Kind ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Equipartition Theorem ◽  
Royal Road ◽  
H Theorem

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.

scholarly journals Correction to: Supply ranges of stone blocks used in masonry bridges and their construction period along the East Royal Road in the Khmer Empire, Cambodia

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Etsuo Uchida ◽  
Yuichiro Sakurai ◽  
Rathborith Cheng ◽  
Ichita Shimoda ◽  
Yu Saito
Keyword(s):  
Construction Period ◽  
Royal Road

Dreams: The royal road to the intestines?

2002 ◽  
Vol 34 (7) ◽  
pp. 468-469
Author(s):  
E.A. Guthrie
Keyword(s):  
Royal Road
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