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There is a current interest in quantum thermodynamics in the context of open quantum systems. An important issue is the consistency of quantum thermodynamics, in particular the second law of thermodynamics, i.e., the flow of heat from a hot…
Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({\cal R})$ gravity as a non-equilibrium one. We apply Eckart's first order thermodynamics to the…
Basic equations of nonequilibrium thermo field dynamics of dense quantum systems are presented. A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev.…
We develop an axiomatic reconstruction of thermodynamics based entirely on two primitive components: a description of what aspects of a system are observed and a reference measure that encodes the underlying descriptive convention. These…
A Hamilton-Jacobi formalism for thermodynamics was formulated by Rajeev [Ann. Phys. 323, 2265 (2008)] based on the contact structure of the odd dimensional thermodynamic phase space. This allows one to derive the equations of state of a…
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…
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of Hamiltonian systems in Classical Mechanics, that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure…
Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum…
An internal energy function of the mass density, the volumetric entropy and their gradients at n-order generates the representation of multi-gradient fluids. Thanks to Hamilton's principle, we obtain a thermodynamical form of the equation…
Thermodynamics and information have intricate interrelations. Often thermodynamics is considered to be the logical premise to justify that information is physical - through Landauer's principle -, thereby also linking information and…
We show that, when we study the coexistence of general relativity with thermodynamics, some physical properties that are usually thought of as holographic and lying in the domain of quantum gravity can actually be accessed even at the…
The Jarzynski equality equates the mean of the exponential of the negative of the work (per fixed temperature) done by a changing Hamiltonian on a system, initially in thermal equilibrium at that temperature, to the ratio of the final to…
We investigate the thermodynamic behavior of open quantum systems through the Hamiltonian of Mean Force, focusing on two models: a two-qubit system interacting with a thermal bath and a Jaynes-Cummings Model without the rotating wave…
We present a simplified model of data flow on processors in a high performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit,…
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
To the student of thermodynamics the most difficult subject is entropy. In this paper we examine the actual, practical application of entropy to two simple systems, the homogeneous slab with fixed boundary values of the temperature, and an…
The aim of this paper is to understand the relation between the canonical Hamilton-Jacobi equation for Maxwell's electrodynamics, which is an equation with variational derivatives for a functional of field configurations, and the covariant…
The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized…
We discuss from a bi-Hamiltonian point of view the Hamilton-Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi-bi-Hamiltonian formulation of Pfaffian type. This property allows us…
Thermodynamic principles are often deceptively simple and yet surprisingly powerful. We show how a simple rule, such as the net flow of energy in and out of a moving atom under nonequilibrium steady state condition, can expose the…