Title: Statistical Mechanics at Strong Coupling: A Bridge between Landsberg’s Energy Levels and Hill’s Nanothermodynamics
Authors: Rodrigo de Miguel 1,* and J. Miguel Rubí2
1 Department of Teacher Education, Norwegian University of Science and Technology, 7491 Trondheim, Norway
2 Department of Condensed Matter Physics, University of Barcelona, 08007 Barcelona, Spain

Figure 1. Illustration of the main features of the three small-system theories. In Landsberg’s theory, the energy levels ε1 of the system (blue sphere) are modified into ε1 due to its interaction with the (red) environment. Statistical mechanics at strong coupling starts with a total Hamiltonian consisting of the environment (red), the system (blue) and the interaction (green); averaging the system and the interaction over the environment results in a temperature-dependent Hamiltonian of mean force H1. Hill’s nanothermodynamics considers the system of interest as if it were surrounded by a macroscopic set of interacting replicas; the interaction causes the effective energy to depart from U and become U.