Zermelo recurrence objection

E287425

argument based on Poincaré recurrence critique of Boltzmann’s H-theorem philosophical objection in statistical mechanics

The Zermelo recurrence objection is a critique of Boltzmann’s H-theorem that argues, using Poincaré recurrence, that a finite mechanical system must eventually return arbitrarily close to its initial state, challenging the idea of a strictly monotonic increase of entropy.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (1)

Label	Occurrences
Zermelo recurrence objection canonical	1

Statements (37)

Predicate	Object
instanceOf	argument based on Poincaré recurrence ⓘ critique of Boltzmann’s H-theorem ⓘ philosophical objection in statistical mechanics ⓘ
addressesQuestion	compatibility of microscopic reversibility with macroscopic irreversibility ⓘ
basedOnAssumption	bounded phase space volume ⓘ deterministic classical mechanics ⓘ finite energy ⓘ
challengesClaim	irreversibility derived from time-reversible microscopic laws ⓘ strictly monotonic increase of entropy in isolated mechanical systems ⓘ
contrastsWith	Boltzmann’s probabilistic justification of the second law ⓘ
critiques	H-theorem ⓘ surface form: Boltzmann’s H-theorem
field	philosophy of physics ⓘ statistical mechanics ⓘ thermodynamics ⓘ
hasConsequence	necessity of probabilistic or coarse-grained notions of entropy ⓘ need to distinguish typical from atypical microstates ⓘ
historicalContext	late 19th century debates on the foundations of thermodynamics ⓘ
implies	a finite mechanical system must eventually return arbitrarily close to its initial state ⓘ entropy cannot be strictly monotonically increasing for all times ⓘ
involves	long-time behavior of dynamical systems ⓘ measure-preserving dynamics ⓘ recurrence times ⓘ
motivatedDiscussion	arrow of time in physics ⓘ foundations of the second law of thermodynamics ⓘ role of initial conditions in statistical mechanics ⓘ
namedAfter	Ernst Zermelo ⓘ
relatedTo	Boltzmann–Gibbs entropy in statistical mechanics ⓘ surface form: Boltzmann entropy Loschmidt reversibility objection ⓘ Poincaré recurrence theorem ⓘ second law of thermodynamics ⓘ statistical interpretation of the second law ⓘ
supportsView	entropy increase is not strictly valid for all times in finite systems ⓘ
usesConcept	Hamiltonian mechanics ⓘ surface form: Hamiltonian dynamics Poincaré recurrence theorem ⓘ finite mechanical system ⓘ phase space ⓘ time-reversal invariance ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

H-theorem → subjectOf → Zermelo recurrence objection ⓘ