REALFAG research group

Master project (30 ECTS): Describing small systems

Systems are always in contact with an environment that influences their energy, volume, and mass. In certain cases, the presence of the environment is of little significance, and, for simplicity, the system may be described as though it were isolated. In other cases, surroundings significantly affect the properties of systems, and external interactions need to be taken into account. Systems subject to the latter scenario may be referred to as small, where small is not an attribute determined by the system’s sheer size, but rather by how the size compares to the range of the interactions affecting the system. From this point of view, a solar system may be thought of as small: two adjacent and identical solar systems would not have twice the energy as one solar system. Yet a water droplet may well be thought of as large: a water droplet has roughly twice the internal energy as a droplet half the size.

In contrast to macroscopic systems, small systems are non-extensive, i.e. doubling the size of the system does not simply double its energy. And, as a result, non-additive, i.e. the energy of the system cannot be expressed as the sum of its parts (interaction energies between parts are far from negligible and must also be accounted for).

In other words, small systems escape the paradigms of classical thermodynamics. They don’t follow  and the resulting Euler equation. Yet many such systems are still too large to be conveniently described by quantum theory. Too small for classical thermodynamics and too large for quantum theory. It appears a modified thermostatistical description is in order.

In this master project, the student will identify different approaches to this problem, and how they can help us model the seemingly anomalous properties exhibited by small systems.

The student must be familiar with quantum, statistical and thermal physics or physical chemistry (TFY2045+TFY4230+TFY4165 or TKJ4170+TKJ4215+TKJ4162 or equivalent coursework). Depending on which direction the project takes, it could be an advantage if the student has experience with electronic structure calculations (TKJ4170). Before starting the project, the student will make him/herself familiar with this recent publication: Nanomaterials 2020, 10(12), 2471.

It is expected that the student will invest a minimum of 700-800 hours from his/her start in the project to the oral defense.

Interested students may send their academic profile (with a list of relevant coursework) and a statement of motivation to rodrigo.demiguel@ntnu.no. Other inquiries may be directed at the same address.