The definition of the thermodynamic entropy in statistical mechanics

A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new equilibrium values goes to a narrow peak. Defining the entropy by the logarithm of the probability distribution automatically makes it a maximum at the equilibrium values, so it satisfies the Second Law. It also satisfies the postulates of thermodynamics. Objections to this definition by Dieks and Peters are discussed and resolved. (C) 2016 Elsevier B.V. All rights reserved.