In a novel approach to understanding thermodynamics, a team of researchers from the Federal University of ABC in Brazil has applied a technique from quantum mechanics to the study of equilibrium thermodynamics. The team, led by Luis F. Santos, has formulated a method to treat thermodynamic variables as conjugate pairs of coordinates and momenta, similar to how variables are treated in quantum mechanics. This approach allows for the promotion of extensive and intensive quantities to operators in a Hilbert space, a fundamental concept in quantum mechanics.
The researchers have applied this canonical quantization method to three different systems: the ideal gas, the van der Waals gas, and the photon gas. For the ideal gas, they derived a Schrödinger-like equation where entropy plays the role of time, and the wave function acquires a phase determined by the internal energy. This is a significant result as it bridges the gap between two seemingly different fields: quantum mechanics and thermodynamics.
The team also introduced a pseudo-Hermitian framework to restore the Hermiticity of the temperature operator and established the equivalence among constraint realizations. This framework is crucial in ensuring the mathematical consistency of the approach. The researchers suggest that this method could lead to thermodynamic uncertainty relations, which are analogous to the Heisenberg uncertainty principle in quantum mechanics.
Moreover, the approach could be extended to study quantum and topological phase transitions, as well as black-hole and non-equilibrium thermodynamics. These extensions could have significant implications for the energy industry, particularly in the development of new materials and technologies for energy storage and conversion.
The research was published in the journal Physical Review E, a prestigious journal in the field of statistical, nonlinear, and soft matter physics. The work represents a significant advancement in the understanding of thermodynamics and its connection to quantum mechanics, with potential applications in various fields, including the energy sector.
This article is based on research available at arXiv.