Related papers: Composable entropy and deviation from macroscopic …
To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra…
Entropy functions played a key role in the development of mathematical theory for hyperbolic conservation laws. The notion of entropy, which is intimately connected with symmetry, is an extension \emph{imposed} on nonlinear systems of…
We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially described by a canonical equilibrium distribution.…
The microscopic derivation of the second law for macroscopic system is given under the phenomenological assumption that both the initial and final states are described by mutually different canonical ensembles. In particular, it is also…
We consider thermodynamic systems with finitely many degrees of freedom and subject to an external control action. We derive some basic results on the dependence of the relative entropy production rate on the controlling force. Applications…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…
Comparison of the thermodynamic entropy with Boltzmann's principle shows that under conditions of constant volume the total number of arrangements in simple thermodynamic systems with temperature-independent heat capacities is TC/k. A…
A simple procedure for obtaining superpositions of macroscopically distinct states is proposed and analyzed. We find that a thermal equilibrium state can be converted into such a state when a single global measurement of a macroscopic…
Ordinary, macroscopic systems, naturally tend to a state of maximum entropy compatible with their constraints. However, this might not hold for gravity-dominated systems since their entropy may increase without bound unless this is…
The entropy production rate is a key quantity in non-equilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress towards its full grasping. By…
An attempt is made to construct composable composite entropy with different $q$ indices of subsystems and address the H-theorem problem of the composite system. Though the H-theorem does not hold in general situations, it is shown that some…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
The validity of the Second Law of thermodynamics, indisputable in the macroscopic world, is challenged at the mesoscopic level: a mesoscopic isolated system, possessing spatial dimensions of the order of a few microns, is capable, as shown…
Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a long-outstanding puzzle. Best candidate theories based on the maximum entropy production principle could not be unequivocally proven, in part due to…
We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity, in the general theory, is useful to provide stability of viscous solutions and yields a…
We consider a wide class of linear stochastic problems driven off the equilibrium by a multiplicative asymmetric force. The force brakes detailed balance, maintained otherwise, thus producing entropy. The large deviation function of the…
Nonadditive composition rules for several physical quantities are treated in thermodynamics. It is argued that the zeroth law defines the existence of their additive forms, the formal logarithms. A further principle, the universal…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct…