The fundamental laws governing heat and work, which have informed the design of devices from car engines to refrigerators for over two centuries, are undergoing a significant mathematical re-evaluation. Researchers are now attempting to place the theory of thermodynamics on a more rigorous mathematical footing by employing 'gauge theory', a concept more commonly associated with the complex world of quantum fields.
Thermodynamics is one of the most relatable branches of physics, deeply embedded in our daily lives through technologies that harness or manage heat. Its development was significantly influenced by engineers seeking to enhance the efficiency of heat engines. However, despite its practical success, the theory has long been noted for its mathematical imprecision, according to Bryan Roberts at the London School of Economics and Political Science.
Roberts is spearheading an effort to rebuild thermodynamics using mathematical ideas rooted in geometry and quantum field theory. Central to this innovative approach is gauge theory, which typically addresses properties that are not directly observable or manipulable. He explains this by drawing a parallel to marbles with hidden internal colours; while their motion (observable space) can be measured, their internal colours (unobservable bundle space) are distinct but intrinsically linked.
Applying this to thermodynamics, Roberts posits that the theory operates on two levels: an 'accessible' level involving quantities like a piston's movement, from which work can be extracted, and a less 'accessible' level, such as the heat generated or lost within a system, which cannot be directly manipulated. Traditional thermodynamics treats 'work' and 'heat' equally when accounting for energy changes. However, Roberts's new framework places the 'hidden' nature of the heat component within the 'bundle space' of gauge theory, giving it distinct mathematical weight.
This re-conceptualisation allows researchers to leverage established proofs and insights from gauge theory in other areas of physics to deepen the understanding of thermodynamics. For instance, fundamental thermodynamic quantities like temperature and entropy can now be defined through specific geometric projections from the bundle space to the observable space. Roberts suggests this offers a more geometric definition of entropy, potentially making it more broadly applicable across a vast range of systems, from engines to black holes.
The implications of this theoretical shift could extend beyond abstract mathematics. Gauge structures have previously been linked to experimental observations in the quantum theory of electromagnetic fields. Roberts anticipates a similar outcome for thermodynamics, noting that preliminary experiments involving certain molecular junctions show hints of a thermodynamic version of the Aharonov-Bohm effect – a quantum phenomenon where a charged particle is influenced by a hidden magnetic field. This suggests the potential for future experimental validation of this re-imagined thermodynamic framework.