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 μdN 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.