We review the application of statistical mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent teacher of the same architecture is analyzed. The best possible generalization ability is determined exactly, through the use of a variational method. The construc...

In part I of these lecture notes, I introduce the basic tools of non equilibrium statistical mechanics: linear response, Brownian motion, Langevin equation, (Pauli) master equation. Part II is devoted to a derivation of quantum master equations from the Schrödinger equation, and to some of their applications to quantum optics and to Brownian motion. Finally, in part III, I examine more recent d...

2 Thermodynamics 4 2.1 The Foundations of Thermodynamics . . . . . . . . . . . . . . . 4 2.2 Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . 5 2.3 The Conditions for Equilibrium . . . . . . . . . . . . . . . . . . . 7 2.4 The Equations of State . . . . . . . . . . . . . . . . . . . . . . . . 13 2.5 Thermodynamic Processes . . . . . . . . . . . . . . . . . . . . . . 14 2.6 Ther...

Systems in stationary nonequilibrium are mechanical systems subject to nonconservative external forces and to thermostat forces which forbid indefinite increase of the energy and allow reaching statistically stationary states. A system Σ is described by the positions and velocities of its n particles X, Ẋ, with the particles positions confined to a finite volume container C0. If X = (x1, . . .,...

The field of thermodynamics is easiest to understand in the context of Newtonian mechanics. Newtonian mechanics describes the effect of forces on objects. Thermodynamics describes the effect of heat transfer on objects. When heat is transferred,the temperature of an object changes.Temperature and heat are also intimately related to energy. A hot gas in a piston has a high pressure and it can do...

Ideas by Statistical Mechanics (ISM) is a generic program to model evolution and propagation of ideas/patterns throughout populations subjected to endogenous and exogenous interactions. The program is based on the author’s work in Statistical Mechanics of Neocortical Interactions (SMNI), and uses the author’s Adaptive Simulated Annealing (ASA) code for optimizations of training sets, as well as...

Without attempting to summarize the vast field of statistical mechanics, we briefly mention some of the progress that was made in areas which have enjoyed Barry Simon’s interests. In particular, we focus on rigorous non-perturbative results which provide insight on the spread of correlations in Gibbs equilibrium states and yield information on phase transitions and critical phenomena. Briefly m...

" O! immodest mortal! Your destiny is the joy of watching the evershifting battle! " Ludwig Boltzmann † Lecture given at the International Meeting " Boltzmann's Legacy-150 Years after his Birth " , organized by the Accademia Nazionale dei Lincei, 25-28 May 1994, in Rome, to be published in: " Atti dell " Accademia Nazionale dei Lincei " , 1997.