This year marks the 150th anniversary of the concept of entropy, introduced into thermodynamics by Rudolf Clausius. Despite its central role in the mathematical formulation of the Second Law and most of classical thermodynamics, its physical meaning continues to be elusive and confusing. This is particularly the case when one invokes the connection between the classical thermodynamics of a system and the statistical behavior of its constituent microscopic particles.

This paper sketches Clausius approach to its definition and offers a modified mathematical definition that is still in the spirit of Clausius’ derivation. In the modified version, the differential of specific entropy appears as a non-dimensional energy term that captures the invigoration or reduction of microscopic motion upon addition or withdrawal of heat from the system. It is also argued that heat transfer is a better thermodynamic model process to illustrate the concept of entropy instead of the canonical heat engines and refrigerators that are not relevant to new areas of thermodynamics (e.g. thermodynamics of biological systems). In this light, it is emphasized that entropy changes, as invoked in the Second Law, are necessarily related to the non-equilibrium interactions of two or more systems that might have initially been in thermal equilibrium but at different temperatures. The overall direction of entropy increase indicates the direction of naturally occurring heat transfer processes in an isolated system of internally interacting (non-isolated) sub systems.

We discuss the implication of the proposed modification on the interpretation of entropy in statistical thermodynamics as well as the formulation of the most common thermodynamic potentials.