Empathiom

Empathiom (also translated as empathion and empathium) are a sort of energy source that the Travelers are seeking for their creators. The world of Theldesia is ripe with it after the Catastrophe, an event that the Travelers detected and thus purposely involved themselves with in order to harvest it.

Overview
While the true nature of empathiom is unknown, it is very likely that it takes the form of memories -- particularly the memories sacrificed by Adventurers to revive after death. As a result, the Genius are often seen trying to spread death and destruction in order to acquire more empathiom.

When on Mare Tranquillitatis, Shiroe and Akatsuki saw glass-like shards rising from the sea, which are actually empathiom crystals, transformed from the snippets of hair Adventurers had cut off to symbolize their (forced) desire to return to the real world.

Minori is the first to hear about such a thing, after questioning Roe2 about her true nature. Roe2 is also mentioned to have a Sacrament-level item, an item class that never existed prior to the Catastrophe, that contains a piece of empathiom that contains a girl's voice teaching the meaning of the word "irreplaceable".

Etymology
The kanji used, 共感子, transliterates "empathy child". The name in ruby characters, エンパシオム, has no clear translation; however, it is obviously supposed to invoke the word "empathy" and thus, feelings.

On Mare Tranquillitatis, both Shiroe and Akatsuki note that before sacrificing their memories in order to revive, they felt a strong urge to revive and try over again. Although they can rationalize to themselves why they wanted to, it is suggested that this feeling is forced upon them. There is no other reason why the members of the Odyssea Knights always revive after dying, since it was explicitly stated that they die on purpose in order to catch a glimpse of the old world. However, Roe2 notes that the Odyssea Knights, by dying constantly and sacrificing memories to revive, are furthering the Genius' plan, which adds to the theory that the desire to revive is forced upon those who die.