There are at least two board games known under the name Entropy, one invented by Eric Solomon and published in 1977, the other by Augustine Carreno in 1994. Both are two-player abstract strategic games played on square boards.

Solomon's game is played on a square board divided into 7x7 cells where one player ("Order") is trying to make patterns while his opponent ("Chaos") is trying to prevent this. The game has been included as one of the events at the annual Mind Sports Olympiad ever since its inception and is marketed under the names "Hyle" (for a simplified version played on a 5x5 board) and "Hyle7".

Carreno's game is played on a square board divided into 5x5 cells. Here for each player the object is to be first to go from the initial position, in which all the player's pieces can move, to a position in which none can. A piece is enabled to move only when it is in contact, horizontally, vertically or diagonally with at least another piece of the same type. This is one of the games that can be played by email via Richard Rognlie's Play-By-eMail Server.


Reference
The full game rules for Solomon's game are available from the Mind Sports Worldwide home page. 
The full game rules for Carreno's game are available from Richard Rognlie's Play-By-eMail Server.