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.