Seminar Details
2021-02-16 (14h) : Markov Chains in Physics: Thermodynamic Uncertainty Relations and the Paradox of the Diode
At MS Teams
Organized by Mathematical Engineering
Speaker :
Delvenne, Jean-Charles
Abstract :
Many microscopic phenomena can be adequately modelled with Markov chains. We will review briefly how the chief concepts of statistical physics such as entropy production, heat, energy are expressed as Markov-chain-theoretic quantities. Within this formalism, we study two specific problems of recent interest, depending on time and interaction with the audience: 1) First we formulate and prove a general Thermodynamic Uncertainty Relation, ie a relation showing that an observable of interest (e.g. total work or heat or displacement over the cycle of an engine) must have a high variance unless a lot extra power is spent: 'precision is costly'. A motivating example is the kinesin, a protein which transports material across the cell. 2) Brillouin's paradox, or the Paradox of the Diode, states that a diode could apparently rectify the positive and negative fluctuations of the thermal noise into an always-positive voltage source, thus extracting useful energy from noise. To solve this paradox, one must accept that the behaviour of a device cannot be defined independently of its environment: the Principle of Modularity is violated at microscopic scale. With this model in mind, we can derive novel models of MOS transistors and CMOS gates subject to thermal noise.