On Prigogine's approaches to irreversibility: a case study by the baker map.
On the classical and quantum evolution of lagrangian half-forms in phase space
On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics
We study the zero-temperature limit for Gibbs measures associated to Frenkel–Kontorova models on . We prove that equilibrium states concentrate on configurations of minimal energy, and, in addition, must satisfy a variational principle involving metric entropy and Lyapunov exponents, a bit like in the Ruelle–Pesin inequality. Then we transpose the result to certain continuous-time stationary stochastic processes associated to the viscous Hamilton–Jacobi equation. As the viscosity vanishes, the...