Entropy of Isolated System

many of us referred that ISOLATED system has an entropy greater than or equal to 0. in this system, entropy of surroundings is zero. there is no heat reactions that takes place with surroundings. i mean those reactions are internal reactions. so entropy is zero. but why it consider to be grater than 0?
- ashik (age 21)
delhi,India

Your question about the entropy of an isolated system raises profound issues. I'll try to convey what little i understand about them. You might read this old answer for background:  .

Let's start with a system that is almost isolated, but not quite exactly. It gradually gets entangled with the outside world, meaning that its state can no longer be fully specified internally, since what state it's in depends on what state the outside is in. That means that the purely internal description requires some probabilities for different states, i.e. a "density matrix", and thus has entropy. As entanglement with the outside grows, the internal entropy increases. Zurek has argued that for very nearly isolated systems the growth of the internal entropy is determined by internal dynamics, not dependent on details of the tiny interaction with the outside.

What if we include more stuff in our system, until we have a truly isolated system, with zero interactions with the outside? If the universe is infinite, that doesn't work because of long-range interactions (e.g. gravity) with the distant outside. 

Depending on cosmological pictures, even a nominally closed universe may not be environment-free. Sean Carroll has argued that universes shed baby universes by quantum fluctuations, which would mean entanglement with an outside is unavoidable.

Mike W.

(published on 08/03/2015)