ﻻ يوجد ملخص باللغة العربية
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 $I={I^{i}}$; 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 $Delta I^{i}Delta eta_{i}geq k$. Here, $k$ is the Boltzmanns constant, $eta_{i}=partial mathcal{S}(I|theta)/partial I^{i}$ are the restituting generalized forces derived from the entropy $mathcal{S}(I|theta)$ of a closed system, which is found in an equilibrium situation driven by certain control parameters $theta={theta^{alpha}}$. 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 $dp(I|theta)simexp[mathcal{S}(I|theta)/k]dI$ appears as the correspondence principle between classical statistical mechanics and thermodynamics in the limit $krightarrow0$, while the existence of uncertainty relations can be associated with the non-commuting character of certain operators.
We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular emphasis
Boltzmanns ergodic hypothesis furnishes a possible explanation for the emergence of statistical mechanics in the framework of classical physics. In quantum mechanics, the Eigenstate Thermalization Hypothesis (ETH) is instead generally considered as a
The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfi
Recently, we have presented some simple arguments supporting the existence of certain complementarity between thermodynamic quantities of temperature and energy, an idea suggested by Bohr and Heinsenberg in the early days of Quantum Mechanics. Such a
The local equilibrium approach previously developed by the Authors [J. Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their loc