Dr Faustus of Modern Physics - Department of Speech, Music and ...

Chapter 22
Loschmidt’s Reversibility
Paradox
Since a given system can never of its own accord go over into another
equally probable state but into a more probable one, it is likewise
impossible to construct a system of bodies that after traversing various
states returns periodically to its original state, that is a perpetual
motion machine. (Boltzmann)
The Translators foreword to Lectures on Gas Theory by Boltzmann, confesses
• There is apparently a contradiction between the law of increasing entropy
and the principles of Newtonian mechanics, since the latter do
not recognize any difference between past and future times. This is the
so-called reversibility paradox (Umkehreinwand) which was advanced as
an objection to Boltzmann’s theory by Loschmidt 1876-77.
Loschmidts paradox formulated in 1876 by Johann Josef Loschmidt, compares
the time-reversibility of Hamiltonian systems with the irreversibility of
the 2nd Law of thermodynamics:
If microscopically matter consists of atoms and molecules ruled by reversible
Hamiltonian mechanics, from where does the irreversibility of macroscopic
physics? This was the problem Boltzmann set out to solve in his 1877
article
• On the Relation of a General Mechanical Theorem to the Second Law
of Thermodynamics,
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