2012/03/06 by L. Velazquez, Luisberis Velazquez Abad · 18 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analytical dynamics #Classical limit #Classical physics #Complementarity (molecular biology) #Complex Systems and Dynamics #Einstein #Entropy (arrow of time) #Observable #Quantum statistical mechanics #Statistical Mechanics and Entropy #Statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.aop.2012.03.002
published in Annals of Physics 327(6), 1682-1693 (Elsevier BV) · 8 pages, no figure; elsart style. Version accepted in Annals of Physics
arxiv created 2012/03/06 · openalex publication_date 2012/03/17 · arxiv updated 2013/07/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the complementarity between two descriptions that are unified in thermodynamics: (i) the parametrization of the system macrostate in terms of mechanical macroscopic observables I=\Ii\; and (ii) the dynamical description that explains the evolution of a system towards the thermodynamic equilibrium. As expected, such a complementarity is related to the uncertainty relations of classical statistical mechanics ΔIiΔηi≥ k. Here, k is the Boltzmann's constant, ηi=∂ S(I|θ)/∂ Ii are the restituting generalized forces derived from the entropy S(I|θ) of a closed system, which is found in an equilibrium situation driven by certain control parameters θ=\θα\. These arguments constitute the central ingredients of a reformulation of classical statistical mechanics from the notion of complementarity. In this new framework, Einstein postulate of classical fluctuation theory dp(I|θ)∼exp[S(I|θ)/k]dI appears as the correspondence principle between classical statistical mechanics and thermodynamics in the limit k→0, while the existence of uncertainty relations can be associated with the non-commuting character of certain operators.