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Preliminary remarks The model Programme two particles finitely many particles heat conduction A heat conduction model with localized billiard balls and weak interaction forces Imre P eter T oth University of Helsinki, Budapest

  1. Preliminary remarks The model Programme two particles finitely many particles heat conduction A heat conduction model with localized billiard balls and weak interaction forces Imre P´ eter T´ oth University of Helsinki, Budapest University of Technology Hyperbolic Dynamical Systems in the Sciences INdAM, Corinaldo, June 3, 2010

  2. Preliminary remarks The model Programme two particles finitely many particles heat conduction Preliminary remarks Motivation: Gaspard-Gilbert model work in progress – more phenomena than complete proofs Carlangelo Liverani will (also) talk about something very similar tomorrow I apologize for my first beamer presentation

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  4. Preliminary remarks The model Programme two particles finitely many particles heat conduction Goal Understand heat conduction T t0 T t1 t2 heat current x x big system + thermostats, or infinite system + nenequilibrium initial conditions Temperature defined e.g. as expectation of energy, or T = 1 /β if energy ∼ e − β E

  5. Preliminary remarks The model Programme two particles finitely many particles heat conduction Dreams Dreams: Fourier’s law ∂ t T ( t , x ) = −∇ x J ( t , x ) J ( t , x ) = D ( T ( t , x )) ∇ x T ( t , x ) not obviously true: models with“not enough nonlinearity” exhibit anomalous heat conduction out of reach for this system at the moment

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