\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Entropy

There are certain physical processes which are irreversible: they only occur in a single direction in time:

• A cup may shatter on the ground, but the pieces will never reassemble themselves again.
• A spritz of perfume will fill a room but not gather back up into one corner.
• Heat only flows from hotter to colder objects, never in reverse.

What these processes have in common is that they all increase entropy.

Entropy is a measure of how disordered a system is, or of how many different ways its components can be rearranged. There is only one way for the pieces to be a cup, but many ways for the pieces to be arranged as pieces. One formulation of the Second Law of Thermodynamics says that

This is what makes an irreversible process irreversible: it involves an increase of the system’s entropy.

A closed system is one which does not exchange energy with its environment. For example, it is certainly possible for you to reassemble the pieces of the cup and glue it back together: by doing work on the cup you are able to decrease its entropy, as it is no longer a closed system. However, your own entropy increases (by turning food into energy) and the total entropy of the closed system of you plus the cup does increase.