Related papers: The Gibbs "volume" entropy is incorrect
Temperature of a finite-sized system fluctuates due to the thermal fluctuations. However, a systematic mathematical framework for measuring or estimating the temperature is still underdeveloped. Here, we incorporate the estimation theory in…
The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of…
We present a unified approach to thermodynamic description of one, two and three dimensional phases and phase transformations among them. The approach is based on a rigorous definition of a phase applicable to thermodynamic systems of any…
The connection between gravity and thermodynamics is explored. Examining a perfect fluid in gravitational equilibrium we find that the entropy is extremal only if Einstein's equations are satisfied. Conversely, one can derive part of…
The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time $t$. Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed…
In order to undestand how the complex concept of entropy emerged,we propose a trip towards the past reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since the Gibbs's work is not very well known, we present a…
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…
Here we explain how C. Tsallis' reply (Entropy 2021, 23(5), 630) fails to respond to points raised in (Entropy 2020, 22(10), 1110) and introduces further inconsistencies on the origin of black hole entropy. In his reply, Tsallis argues that…
This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are mis-cible, the mixture is subjected to a non-symmetric constraint on the volume. Adopting the Gibbs…
We show that the mathematical structure of Gibbsian thermodynamics flows from the following simple elements: the state space of a thermodynamical substance is a measure space together with two orderings (corresponding to "warmer than" and…
Internal energy, enthalpy and entropy are the key quantities to study thermodynamic properties of the moist atmosphere, because they correspond to the First (internal energy and enthalpy) and Second (entropy) Laws of thermodynamics. The aim…
The notion of mean temperature is crucial for a number of fields including climate science, fluid dynamics and biophysics. However, so far its correct thermodynamic foundation is lacking or even believed to be impossible. A physically…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of…
If the negative cosmological constant is treated as a dynamical pressure and if the volume be its thermodynamically conjugate variable then the gravitational mass can be expressed as the total gravitational enthalpy rather than the energy.…
A first principles analysis of an open system thermodynamical Carnot cycle is provided, and the results are compared to those proposed by Gibbs for open systems. The Kelvin-Clausius statement concerning heat transfer for reversible cycles…
This paper is motivated by the recent paper M. Baldovin, S. Iubini, R. Livi and A. Vulpiani, Statistical mechanics of systems with negative temperature, arXiv:2103.12572. The authors suggest that negative absolute temperatures are…
For the Fermi gas filling the space inside a cubic cavity of a fixed volume, at arbitrary temperatures and number of particles, the thermodynamic characteristics are calculated, namely: entropy, thermodynamic potential, energy, pressure,…
We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All…
We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the…