Testing the Minimum System Entropy and the Quantum of Entropy

Abstract

Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropykln2 and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy kln2. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature.

A Maximum Entropy Resolution to the Wine/Water Paradox

“…It is worth mentioning (with thanks to the anonymous referee who pointed this out) that the standard way of measuring the entropy S of a system is to measure its chemical potential μ and then use the appropriate Maxwell relation (∂ S /∂ n ) T = (∂μ/∂ T ) n , where the number of particles n in the system is assumed to be very large so that the infinitesimals are approximated reasonably well. In this way, one can obtain an ‘ entropy per particle ’ for the system [ 30 ]. But again, to obtain the chemical potential, one usually uses a Lagrange multiplier method and sets it to zero (to effect the ‘equilibrium’ condition).…”