What phenomenon causes a pen to dry out and how does putting the cap on prevent it?

Understanding why pen caps prevent drying involves physics of evaporation and latent heat. Evaporation is an endothermic process. This causes the pen to feel cool. When the cap is placed on the pen the small enclosed air space quickly becomes saturated with ink vapour (reaches 100% relative humidity with respect to ink). At saturation evaporation stops because the air cannot hold any more vapour. Ink does not freeze inside a pen at normal room or even outdoor temperatures. Ink has antifreeze properties and remains liquid well below 0 degrees C. Warmth from cap is not the mechanism as caps are not heated. The cap does not create significant pressure inside. The tiny air gap sealed by a cap does not build up measurable pressure. If pressure were the mechanism uncapped pens would dry immediately which happens slowly. While oxygen can eventually react with some ink components this chemical oxidation is not the primary mechanism of pen drying. The primary cause is evaporation of the ink solvent.