The geometric study of thermodynamics began with Gibbs’s reformulation of the theory in terms of equilibrium states rather than processes [1]. The surface of the set of equilibrium states was Gibbs’s primary object of study and foreshadowed much of the modern differential geometric theory manifolds. Gibbs surfaces is where the geometric theory stood when I became a graduate student. The story t...

The Witt construction describes a functor from the category of Rings to the category of characteristic 0 rings. It is uniquely determined by a few associativity constraints which do not depend on the types of the variables considered, in other words, by integer polynomials. This universality allowed Alain Connes and Caterina Consani to devise an analogue of the Witt ring for characteristic one,...

The thermodynamic formalism for rotating black holes, characterized by noncommutative and quantum corrections, is constructed. From a fundamental thermodynamic relation, the equations of state and thermodynamic response functions are explicitly given, and the effect of noncommutativity and quantum correction is discussed. It is shown that the well-known divergence exhibited in specific heat is ...

The holographic principle states that the information about a volume of a system is encoded on the boundary surface of the volume. Holography appears in many branches of physics, such as optics, electromagnetism, many-body physics, quantum gravity, and string theory. Here we show that holography is also an underlying principle in thermodynamics, a most important foundation of physics. The therm...

Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of field stochastic and quantum thermodynamics, ideas thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics statistics, optimal transport theory concerns by which one can optimally source distribution tar...

The phase diagram of water has been calculated from the TIP4PQ/2005 model, an empirical rigid non-polarisable model. The path integral Monte Carlo technique was used, permitting the incorporation of nuclear quantum effects. The coexistence lines were traced out using the Gibbs–Duhem integration method, once having calculated the free energies of the liquid and solid phases in the quantum limit,...