Related papers: Gibbs, Boltzmann, and negative temperatures
From black hole thermodynamics, the Bekenstein bound has been proposed as a universal thermal entropy bound. It has been further generalized to an entanglement entropy bound which is valid even in a quantum system. In a quantumly entangled…
Regardless of studies and debates over a century, the statistical origin of the second law of thermodynamics still remains illusive. One essential obstacle is the lack of a proper theoretical formalism for non-equilibrium entropy. Here I…
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…
The theory of superstatistics is a generalization of Boltzmann-Gibbs statistical mechanics which admits temperature fluctuations, and generates non-canonical ensembles from the distribution function of these fluctuations. Recently, some…
It is sometimes argued that the unattainability of zero temperature is a consequence of the second law of thermodynamics. Historically, the independence of the unattainability of zero temperature from the second law was proven more than 80…
There are three levels of description in classical statistical mechanics, the microscopic/dynamic, the macroscopic/statistical and the thermodynamic. At one end there is a well-used concept of equilibrium in thermodynamics and at the other…
We extend on ideas from standard thermodynamics to show that temperature can be assigned to a general nonequilibrium quantum system. By choosing a physically motivated complete set of observables and expanding the system state thereupon,…
The controversial existence of negative temperatures has stirred interesting debates that have reached the foundations of thermodynamics, including questions on the second law, the Carnot efficiency and the statistical definition of…
As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically…
In this paper we discuss about the validity of the Shannon entropy functional in connection with the correct Gibbs-Hertz probability distribution function. We show that there is no contradiction in using the Shannon-Gibbs functional and…
Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, where the number of accessible configurations $W(N)$ grows exponentially with the number of degrees of freedom~$N$.…
This short article was submitted to Nature Physics as a Correspondence. The intention was to provide a brief albeit significant criticism of the work of J. Dunkel and S. Hilbert, \textit{Consistent Thermostatistics Forbids Negative Absolute…
Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium…
We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on…
In their paper [arXiv:1403.4299v1], Frenkel and Warren claim that the Gibbs temperature does not characterize thermal equilibrium correctly. We point out the main logical errors in their argument.
Many discussions in the literature of spacetimes with more than one Killing horizon note that some horizons have positive and some have negative surface gravities, but assign to all a positive temperature. However, the first law of…
In statistical mechanics, entropy is defined as a fundamental quantity. However, its unit, J/K, involves that of temperature, which is only subsequently defined - and defined in terms of entropy. This circularity arises with the…
The example provided in the comment [arXiv:0803.2241] concerns a situation where the system is initially at negative temperature. It is known that in such cases the Law of Entropy Decrease holds. Nevertheless, this does not challenge the…
Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct…
Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical…