# Séminaire du LPTMS: Gatien Verley

## Non-equilibrium conductance — Assembly of energy converter

### Gatien Verley (LPT, Bât. 210, Université Paris-Sud)

Stochastic thermodynamic is the appropriated theory to study small non-equilibrium systems modeled by Markov processes. These systems are driven by several heat reservoirs (or work sources) and are crossed by strong energy currents. In this framework and for stationary Markov jump processes, I will introduce the concept of non-equilibrium conductance matrix that connects energy currents and thermodynamic forces, as Onsager matrices do for close-to-equilibrium systems. I will discuss the Thermodynamic Uncertainty Relations (TUR) that generalizes far from equilibrium the fluctuations-dissipation theorem. A central result is that current covariances are bounded from below by the conductance matrix (Loewner partial order). In the close to equilibrium limit, this TUR saturates restoring the fluctuations-dissipation theorem.

Non-equilibrium conductance matrices are also convenient to study energy converters and power efficiency trade-off. In the second part, I will describe an energy converter made of many small interacting elementary machines. This energy converter has many original features that I found inspiring for understanding the physics of non-equilibrium systems :

– emergent strong coupling in the mean-field treatment (as evidenced by the non-equilibrium conductance matrix),

– collective enhancement of efficiency and power,

– dynamical phase transition and emergent ergodicity breaking (non-convex large deviation functions for currents)

– non-typical efficiency fluctuations

**Date/Time : ** 22/01/2019 - *11:00 - 12:00*

**Location : ** LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay

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