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It has been recently proposed that the interpretation of gravity as an emergent, entropic force might have nontrivial implications to cosmology. Here two approaches are investigated: in one, the Friedman equation receives entropic…
Thermodynamics have been applied to astronomy, biology, psychology, some social systems and so on. But, various evolutions from astronomy to biology and social systems cannot be only increase of entropy. When fluctuations are magnified due…
We derive the expression for the entropy production for stochastic dynamics defined on a continuous space of states containing unidirectional transitions. The expression is derived by taking the continuous limit of a stochastic dynamics on…
The emerging field of stochastic thermodynamics extends classical ideas of entropy, heat and work to non-equilibrium systems. One notable finding is that the second law of thermodynamics typically only holds after taking appropriate…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…
The entropy of a spherically symmetric distribution of matter in self-equilibrium is calculated. When gravitational effects are neglected, the entropy of the system is proportional to its volume. As effects due to gravitational…
We investigate a solution of the exactly renormalized Liouville action to foresee the fate of the two-dimensional de Sitter space. We work in the semiclassical region with a large matter central charge $c$. Instead of de Sitter expansion,…
We develop the framework of classical Observational entropy, which is a mathematically rigorous and precise framework for non-equilibrium thermodynamics, explicitly defined in terms of a set of observables. Observational entropy can be seen…
This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production…
Relating thermodynamic and kinetic properties is a conceptual challenge with many practical benefits. Here, based on first principles, we derive a rigorous inequality relating the entropy and the dynamic propagator of particle…
For an isolated assembly that comprises a system and its surrounding reservoirs, the total entropy ($S_{a}$) always monotonically increases as time elapses. This phenomenon is known as the second law of thermodynamics ($S_{a}\geq0$). Here…
We prove a quantum version of the second law of thermodynamics: the (quantum) Boltzmann entropy increases if the initial (zero time) density matrix decoheres, a condition generally satisfied in Nature. It is illustrated by a model of…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
Recently, Morrison and Updike showed that many dissipative systems are naturally described as possessing a Riemann curvature-like bracket, which similar to the Poisson bracket, generates the dissipative equations of motion once suitable…
In view of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
Some thermodynamic quantities of nonrelativistic ideal boson and fermion gases in the static Taub universe are derived to first order in a small anisotropy parameter d which measuring the deformation from the spherical Einstein universe.…
We consider a boson gas on the stretched horizon of the Schwartzschild and Kerr black holes. It is shown that the gas is in a Bose-Einstein condensed state with the Hawking temperature $T_c=T_H$ if the particle number of the system be equal…
A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy…
The stratification of entropy and the stratification of angular momentum are closely analogous. Of particular interest is the behavior of disks in which angular momentum transport is controlled by convection, and heat transport by dynamical…