Electronic Resource
Springer
Foundations of physics
6 (1993), S. 327-337
ISSN:
1572-9524
Keywords:
Hamiltonian mechanics
;
constant of the motion
;
entropy
;
nonequilibrium thermodynamics
;
Poincaré recurrence theorem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract This note addresses a problem of nineteenth century applied mathematics—is it possible in the context of Hamiltonian mechanics to define a functionS of the generalized coordinates and momenta which is monotonically increasing along orbits? The question is of interest, because, for a sytem not in thermodynamic equilibrium, entropy should increase strictly monotonically along an orbit, and a negative answer implies that mechanical principles different from those of Hamiltonian mechanics must be introduced to explain thermodynamics. This note answers the question rigorously for Hamiltonian systems confined to an invariant region of finite volume in phase space; it is not possible to define a continuous function which increases monotonically along orbits. An appendix gives a translation of an 1889 paper of Poincaré addressing the same issue.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00665652
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