Related papers: A Hamilton-Jacobi Formalism for Thermodynamics
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…
We investigate the relationship between ground-state (zero-temperature) quantum phase transitions in systems with variable Hamiltonian parameters and classical (temperature-driven) phase transitions in standard thermodynamics. An analogy is…
We prove that, contrary to the common belief, the classical Maxwell electrodynamics of a point-like particle may be formulated as an infinite-dimensional Hamiltonian system. We derive well defined quasi-Hamiltonian which possesses direct…
This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton--Jacobi theory. The relation with the "classical" Hamiltonian approach using canonical transformations is also…
We review recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. In this approach,…
In open systems with strong coupling, the interaction energy between the system and the environment is significant, so thermodynamic quantities cannot be reliably obtained by traditional statistical mechanics methods. The Hamiltonian 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…
We review the construction of the universal Hamilton-Jacobi counterterm for dilaton gravity in two dimensions, derive the corresponding result in the Cartan formulation and elaborate further upon black hole thermodynamics and semi-classical…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
We show that when the thermal wavelength is comparable to the spatial size of a system, thermodynamic observables like Pressure and Volume have quantum fluctuations that cannot be ignored. They are now represented by operators; conventional…
The thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state. The black hole mass…
The thermodynamic properties of dark energy-dominated universe in the presence of a black hole are investigated in the general case of a varying equation-of-state-parameter $w(a)$. We show that all the thermodynamics quantities are regular…
Considering an arbitrary, varying equation of the state parameter, the thermodynamic properties of the dark energy fluid in a semiclassical loop quantum cosmology scenario, which we consider the inverse volume modification, is studied. The…
The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…
We consider the Hamiltonian mechanics and thermodynamics of an eternal black hole in a box of fixed radius and temperature in generic 2-D dilaton gravity. Imposing boundary conditions analoguous to those used by Louko and Whiting for…
In this note we discuss the application of the Hamilton-Jacobi formalism to the first order description of four dimensional spherically symmetric and static black holes. In particular we show that the prepotential characterizing the flow…
The physical variables of classical thermodynamics occur in conjugate pairs such as pressure/volume, entropy/temperature, chemical potential/particle number. Nevertheless, and unlike in classical mechanics, there are an odd number of such…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
We discuss the consequences of unique symmetry of de Sitter spacetime, which is invariant under the modified translations, ${\bf r}\rightarrow {\bf r} -e^{Ht}{\bf a}$, where $H$ is the Hubble parameter. Due to this symmetry, all the…