Jean-Charles Delvenne (UCLouvain)

We look at the following motivating problem: how to move an electronic memory from a ‘zero’ state to a ‘one’ state, at minimal energy cost?

Mathematically, this amounts to design a Markov chain  that drives a certain probability measure (encoding a ‘zero’) towards another one (a ‘one’) through an ‘optimal’ path — an avatar of Gaspard Monge’s so-called ‘earth mover problem’, at the core of transport theory.

 We explore various recent results and conjectures around this theme at the interface of statistical physics and Markov chain theory. We support these by illustrations on realistic simulations on electronic memories.