Entropy is defined as a measure of the disorder (randomness) of a system. As such it is a very basic concept which is not confined to only thermodynamic systems. Consider a jar filled with equal numbers of black and white marbles. The black marbles are at the bottom of the jar. Shake the jar and we increase the entropy since some white marbles are now where blacks were and vice versa. The order of the system has been changed.
Using statistical mechanics equations representing the three laws of thermodynamics can be derived using only pure mathematics without any reference to physical reality.