Work of breathing is the energy expended by one breath.
$$\Delta E = \int P dV$$
Each breath consists of elastic work, inspiratory resistive work, and expiatory resistive work.
Elastic work is done on inspiration against the elastic tissues (lung, chest wall, surface tension). It is stored as elastic potential energy, which is released during expiration (65% of work)
Inspiratory resistive work is the remainder of work during inspiration, which is lost as heat. It is done against tissue resistance and airflow resistance. It is increased at high respiratory rates or with high resistance.
Usually, expiratory resistive work is less than the stored elastic potential energy, so there is no net work during expiration. With active expiration where the intraplueral pressure falls below resting pressure, there is additional resistive work.
Minimizing Elastic WOB
Minimizing resistive WOB
For a given minute ventilation, WOB is minimized by a given respiratory rate. Higher respiratory rates (with lower tidal volumes) decrease elastic work but increase resistive work.