Statistical Chemical Thermodynamics and Energetic Behavior of Counting: Gibbs' Theory Revisited.

One of the major tenets of Gibbs' equilibrium chemical thermodynamics is "counting the number of particles" and introducing the associated chemical potential . This leads to the concept of chemical energy μd N that becomes a part of the total internal energy change in Gibbs' fundamental thermodynamic relation. However, a pure thermomechanical description of a particle system has only two fundamental forms of energy, namely, mechanical work and heat; Gibbs' μ is an emergent concept. Following this perspective, we present an alternative, generalized Gibbs formalism that serves as a statistical theory of emergence: chemical potential is introduced down to the level of individual meso- or even microstates of a system. The research practice in biophysical chemistry since the 1950s epitomizes this perspective, in which the concept of potential of mean force, or conditional free energy, plays a central role. Our theory suggests a generalized "energetic representation" for scientific data that is in the form of counting frequency, which is measured routinely through equilibrium constants in chemistry laboratories.