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The eigenvalue of the hermitic Hamiltonian is real undoubtedly. Actually, The reality can also be guaranteed by the $PT$-symmetry. The hermiticity and the $PT$-symmetric quantum theory both have requirements regarding the boundary…
In this paper, we investigate the validity of the generalized second law of thermodynamics of the universe in the DGP brane world.The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon or the event horizon.…
The status of heat and work in nonequilibrium thermodynamics is quite confusing and non-unique at present with conflicting interpretations even after a long history of the first law in terms of exchange heat and work, and is far from…
Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…
We provide a stochastic mathematical representation for Clausius' and Kelvin-Planck's statements of the Second Law of Thermodynamics in terms of the entropy productions of a finite, compact driven Markov system and its lift. A surjective…
The flow of a thermoelectric current through a semiconductor of submicron dimensions is analyzed. The rate of surface relaxation of the energy is assumed to be much higher than the rate of electron-electron collisions. Under these…
Growing economic inequalities are observed in several countries throughout the world. Following Pareto, the power-law structure of these inequalities has been the subject of much theoretical and empirical work. But their nonequilibrium…
The 2nd law of thermodynamics is used to shed light on present-day puzzles in cosmology. The universal law, given as an equation of motion, describes diverse systems when consuming free energy via various mechanisms to attain stationary…
Thermodynamics allows the application of Statistical Mechanics to finite and even small systems. As surface effects cannot be scaled away, one has to be careful with the standard arguments of splitting a system into two or bringing two…
In this paper, we proved that by choosing the proper variational function and variables, the variational approach proposed by M. Doi in soft matter physics was equivalent to the Conservation-Dissipation Formalism. To illustrate the…
An essential role of information in microscopic thermodynamics (e.g. Maxwell's demon) opens a challenging question if there exists a formulation of the second law of thermodynamics based only on pure information ideas. Here, such a…
Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and Newton's third law are equivalent. However, the demonstration of this fact is usually incomplete in textbooks. We shall…
Jensen's Inequality (JIEQ) has proved to be a major tool to prove the consistency of various fluctuation theorems with the second law in microscopic thermodynamics. We show that the situation is far from clear and the reliance on the JIE…
By using a path information defined for the measure of the uncertainty of instable dynamics, a theoretical derivation of Fourier's law of heat conduction is given on the basis of maximum information method associated with the principle of…
The second law of thermodynamics is known to hold at small scales also when gravity plays a leading role, as in the case of black holes and self-gravitating radiation spheres. It has been suggested that it should as well at large scales.…
Observationally and experimentally, physical laws express how particles interact. Conversely, physical laws should be invariant under any re-arrangement of those particles, e.g., the laws of gravity do not change if one re-arranges the…
To reconstruct thermodynamics based on the microscopic laws is one of the most important unfulfilled goals of statistical physics. Here, we show that the first law and the second law for adiabatic processes are derived from an assumption…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
Misinterpretations of Newton's second law for variable mass systems found in the literature are addressed. In particular, it is shown that Newton's second law in the form $\vec{F} = \dot{\vec{p}}$ is valid for variable mass systems in…
We construct the law of L\'{e}vy processes conditioned to stay positive under general hypotheses. We obtain a Williams type path decomposition at the minimum of these processes. This result is then applied to prove the weak convergence of…