Related papers: A note on Gibbs paradox
Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of $n$ weakly interacting identical subsystems and passage to the…
The problems and paradoxes of the Lifshitz theory in application to real dielectric and semiconductor materials are reviewed. It is shown that the inclusion of drift current of conduction electrons into the model of dielectric response…
The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
We reveal a contradiction in measure-theoretic probability. The contradiction is an "equation" $1/2 = 0$ with its two sides representing probabilities. Unlike known paradoxes in mathematics, the revealed contradiction cannot be explained…
We provide here a thermodynamic analog of the Braess road-network paradox with irreversible engines working between reservoirs that are placed at vertices of the network. Paradoxes of different kinds reappear, emphasizing the specialty of…
Generalization through novel interpretations of the inner logic of the century-old Gibbs' statistical thermodynamics is presented: i) Identifying $k_B\to 0$ as classical energetics, one directly derives a pair of thermodynamic variational…
In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and…
A capacitor paradox is an electromagnetic problem designed to show the limits of circuit theory which considers the connection of two ideal capacitors, one charged and the second discharged. A blind solution to this problem leads to the…
The relationships between reversible Carnot cycles, the absence of perpetual motion machines and the existence of a non-decreasing, globally unique entropy function forms the starting point of many textbook presentations of the foundations…
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…
Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature…
A refinement of an argument due to Maxwell for the equipartition of kinetic energy in a mixture of ideal gases with different masses is proposed. The argument is elementary, yet it may work as an illustration of the role of symmetry and…
The generalized Gibbs free energy and enthalpy is derived in the framework of nonextensive thermodynamics by using the so-called physical temperature and the physical pressure. Some thermodynamical relations are studied by considering the…
In his Comment [1], Philip Strasberg (PS) argues from the analysis of different examples that the framework we have presented in [2] does not recover known results of macroscopic textbook thermodynamics. Here, we show that such apparent…
This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs' paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical…
Macroscopic thermodynamics of equilibrium is constructed for systems obeying power-law canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is…
This article mainly consists in the quantum mechanical study of an adiabatically compressed particle, in an infinitely high well, which we conjecture, can be considered as the basis of an ideal gas. Thus we prove that, all the compression…
We brief{}ly review the connection between statistical mechanics and thermodynamics. We show that, in order to satisfy thermodynamics and its Legendre transformation mathematical frame, the celebrated Boltzmann-Gibbs~(BG) statistical…
We examine the basic assumptions underlying a scenario due to Kibble that is widely used to estimate the production of topological defects. We argue that one of the crucial assumptions, namely the geodesic rule, although completely valid…