Related papers: Geometric properties of qudit systems
Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
We develop a geometric theory of phase transitions (PTs) for Hamiltonian systems in the microcanonical ensemble. This theory allows to reformulate Bachmann's classification of PTs for finite-size systems in terms of geometric properties of…
In the general case of a many-body Hamiltonian system, described by an autonomous Hamiltonian $H$, and with $K\geq 0$ independent conserved quantities, we derive the microcanonical thermodynamics. By a simple approach, based on the…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We develop both…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
The state of a thermodynamic system being characterized by its set of extensive variables $q^{i}(i=1,...,n) ,$ we write the associated intensive variables $\gamma_{i},$ the partial derivatives of the entropy $ S(q^{1},...,q^{n}) \equiv…
Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for…
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime,…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this…
We describe a novel method to obtain thermodynamic properties of quantum systems using Baysian Inference -- Maximum Entropy techniques. The method is applicable to energy values sampled at a discrete set of temperatures from Quantum Monte…
The fabrication, utilisation, and efficiency of quantum technologies rely on a good understanding of quantum thermodynamic properties. Many-body systems are often used as hardware for these quantum devices, but interactions between…
We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by i) the temporal trajectory of…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
This paper presents an introduction to geometric representations of quantum states in which each distinct quantum state, pure and mixed, corresponds to a unique point in a Euclidean space. Beginning with a review of some underappreciated…
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic…
In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of…
Phase diagrams chart material properties with respect to one or more external or internal parameters such as pressure or magnetisation; as such, they play a fundamental role in many theoretical and applied fields of science. In this work,…