Let ent denote topological entropy, and let $C'r(S^1, S^1)$ denote the space of continuous functions of the circle to itself having $r$ continuous derivatives with ...

Exactly 200 years ago, a French engineer introduced an idea that would quantify the universe’s inexorable slide into decay. But entropy, as it’s currently understood, is less a fact about the world ...

According to the second law of thermodynamics, the entropy of an isolated system tends to increase over time. Everything ...

Thermodynamic spontaneity—whether a reaction can go—can be measured by changes in either of two parameters: entropy or free energy.