Related papers: The New Finite Temperature Schrodinger Equation
Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicate details of the microscopic dynamics within a macroscopic system. The strength of Thermodynamics lies in…
It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect…
Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schr\"odinger's equation and the second law of thermodynamics. Despite…
The physical quantity "temperature" is a cornerstone of thermodynamics and statistical physics. But it is necessary to mention that very frequently the scientists forget about the conditions to be satisfied in order to introduce…
We show that the quantum statistical mechanics describing quantum and thermal properties of objects has only the sense of a particular semiclassical approximation. We propose a more general (than that theory) microdescription of objects in…
We review the derivation of quantum theory as an application of entropic methods of inference. The new contribution in this paper is a streamlined derivation of the Schr\"odinger equation based on a different choice of microstates and…
Two different theoretical formulations of the finite temperature effects have been recently proposed for integrable field theories. In order to decide which of them is the correct one, we perform for a particular model an explicit check of…
Schr\"odinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum…
In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic…
Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
In our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], we developed a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities at temperature T,…
In this paper, we search the dependence of some statistical quantities such as the free energy, the mean energy, the entropy, and the specific heat for the Schr\"odinger equation on the temperature, particularly the case of a non-central…
We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical…
A theory of thermodynamics has been recently formulated and derived on the basis of R\'enyi entropy and its relative versions. In this framework, we define the concepts of partition function, internal energy and free energy, and fundamental…
We show how the macroscopic state variables pressure, entropy and temperature of equilibrium thermodynamics can be consistently derived from the (quantum) chaotic spectral structure of one or two particles in two-dimensional domains. This…
We explore the thermodynamics of quantum processes (quantum channels) by axiomatically introducing the free energy for channels, defined via the quantum relative entropy with an absolutely thermal channel whose fixed output is in…
In nature, everything occurs at finite temperature and quantum phase transitions (QPTs) cannot be an exception. Nevertheless, they are still mainly discussed and formulated at zero temperature. We show that the condensation QPTs recently…
Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to approach the issue of…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…