Ensemble and trajectory thermodynamics: A brief introduction

• We review stochastic thermodynamics at the ensemble level.
• We formulate first and second laws at the trajectory level.
• The stochastic entropy production is the log-ratio of trajectory probabilities.
• We establish the relation between the stochastic grand potential, work and entropy production.
• We derive detailed and integral fluctuation theorems.

We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.