A formulation of this quantity due to Kolmogorov is derived by dividing phase space into infinitesimal hypercubes and is equal to an integral of the Lyapunov exponent over possible trajectories. By relaxing the requirement of additivity, Renyi generalized one form of this quantity using a parameter alpha. Von Neumann's formulation of this quantity 
A formulation of this quantity due to Kolmogorov is derived by dividing phase space into infinitesimal hypercubes and is equal to an integral of the Lyapunov exponent over possible trajectories. By relaxing the requirement of additivity, Renyi generalized one form of this quantity using a parameter alpha. Von Neumann's formulation of this quantity sets it proportional to the trace of the density matrix times the natural log of the density matrix, though this quantity is more commonly understood in a Gibbs state and in a form named for Shannon, where it measures the amount of information needed to encode a state. In equilibrium thermodynamics, the Gibbs free energy is equal to the enthalpy minus the temperature times this quantity. For 10 points, name this quantity which, according to the second law of thermodynamics, always rises.
A formulation of this quantity due to Kolmogorov is derived by dividing phase space into infinitesimal hypercubes and is equal to an integral of the Lyapunov exponent over possible trajectories.
{Entropy} [accept {S}]