# Entropy as Sum of Kinetic Energy?

Is it possible to view entropy as the sum of the kinetic energy of all molecules in the system? Since a system with 0 entropy would have 0 motion, and as you increase the motion of the molecules, entropy increases as well. If not, could you provide a simple counterexample in which entropy does not make sense as the sum of kinetic energy?

• You might want to review the concept of entropy, including but not limited to the third law of thermodynamics and the statistical mechanical view of entropy. – Todd Minehardt Feb 8 '17 at 0:47
• I see the classical explanations of entropy as the 'randomness' of a system, but this seems to be a direct contradiction with the units of entropy (Joules/K). – Andi Gu Feb 8 '17 at 0:54
• @AndiGu You have randomness in Boltzmann's description of entropy. S=Boltzmann constant* lnW where W is macrostate multiplicity. But Clausius first described entropy with dS= dq/T which makes it unit J/Kwhich doesn't incorporate randomness. And Boltzmann introduced randomness to the concept of entropy(and it's a classical concept). But I think he could just do with lnW but to get it consistent with a pre-established theory Boltzmann introduced kB to the equation. – Mockingbird Feb 8 '17 at 1:22
• As an example, there is entropy increase upon mixing two substances together or even of mixing up sets of different objects even if both sets are already 'random'. No kinetic energy need be involved. Randomness is an unfortunate term often used to describe entropy. Its the degree of randomness that is described and what this is is not clear in everyday usage so its best totally avoided . Entropy is $S=k\ln(\Omega)$ where $\Omega$ is the number of ways of arranging objects, in molecules this means calculating the number of ways of placing then in all their possible energy levels. – porphyrin Feb 8 '17 at 9:43
• @AndiGu Your view is also a direct contradiction with the units of entropy (Joules/K). These do not match the units of energy (Joules). – Ivan Neretin Feb 8 '17 at 10:09

In a crystal lattice, there are two contributions to the entropy: the vibrational entropy and the configurational entropy. The first is related to the kinetic energy; atoms with higher kinetic energies have tend to have larger displacements from equilibrium, and have a larger "footprint" in phase space, resulting in a higher entropy. The second contribution, configurational entropy, arises from disorder in the crystal lattice, namely the number of ways of arranging the atoms. In a perfect crystal, there is only one way, so the configurational entropy ($k\ln W$) will be 1.