Published in Journal of Physical Chemistry B, 2017, 121 (45), 10429‐10434 1 Thermodynamics Far From the Thermodynamic Limit Rodrigo de Miguel* Department of Teacher Education Norwegian University of Science and Technology, 7491 Trondheim, NORWAY. rodrigo.demiguel@ntnu.no J. Miguel Rubí Departament de Física de la Matèria Condensada, Facultat de Física Universitat de Barcelona, 08029 Barcelona, SPAIN. mrubi@ub.edu Abstract Understanding how small systems exchange energy with a heat bath is important to describe how their unique properties can be affected by the environment. In this contribution, we apply Landsberg's theory of temperature‐dependent energy levels to describe the progressive thermalization of small systems as their spectrum is perturbed by a heat bath. We propose a mechanism whereby the small system undergoes a discrete series of excitations and isentropic spectrum adjustments leading to a final state of thermal equilibrium. This produces standard thermodynamic results without invoking system size. The thermal relaxation of a single harmonic oscillator is analyzed as a model example of a system with a quantized spectrum than can be embedded in a thermal environment. A description of how the thermal environment affects the spectrum of a small system can be the first step in using environmental factors, such as temperature, as parameters in the design and operation of nanosystem properties.