相关论文: Comparison of Thermodynamic Characteristics in Ord…
Using a game theory approach and a new extremal problem, Gibbs formula is proved in a most simple and general way for the classical mechanics case. A corresponding conjecture on the asymptotics of the classical entropy is formulated. For…
Two approaches to describe the thermodynamics of a subsystem that interacts with a thermal bath are considered. Within the first approach, the mean system energy $E_{S}$ is identified with the expectation value of the system Hamiltonian,…
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum…
Basic relations for the mean length and algorithmic entropy are obtained by solving a new extremal problem. Using this extremal problem, they are obtained in a most simple and general way. The length and entropy are considered as two…
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual…
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…
Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the heat quantity, then the value of the Shannon entropy comes to formally…
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
One of the fundamental laws of classical statistical physics is the energy equipartition theorem which states that for each degree of freedom the mean kinetic energy $E_k$ equals $E_k=k_B T/2$, where $k_B$ is the Boltzmann constant and $T$…
Despite well over a century of effort, the proper expression for the classical entropy in statistical mechanics remains a subject of debate. The Boltzmann entropy (calculated from a surface in phase space) has been criticized as not being…
For more than 100 years, one of the central concepts in statistical mechanics has been the microcanonical ensemble, which provides a way of calculating the thermodynamic entropy for a specified energy. A controversy has recently emerged…
Quantum typicality refers to the phenomenon that the expectation values of any given observable are nearly identical for the overwhelming majority of all normalized vectors in a sufficiently high-dimensional Hilbert (sub-)space. As a…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems, made up of microscopic particles, in terms of a small number of macroscopic quantities, such as…
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,…
For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the…
We construct the equation of a state of the classical QGP valid for all values of Gamma=V/K, the ratio of the mean Coulomb to kinetic energy. By enforcing the Gibbs relations, we derive the pertinent pressure and entropy densities for all…
Underlying the classical thermodynamic principles are analogous microscopic laws, arising from the fundamental axioms of quantum mechanics. These define quantum thermodynamic variables such as quantum work and heat and characterize the…
Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs'…