Related papers: On the entropy of classical systems with long-rang…
This paper proposes a theory that bridges classical analytical mechanics and nonequilibrium thermodynamics. Its intent is to derive the evolution equations of a system from a stationarity principle for a suitably augmented Lagrangian…
Isolated quantum systems follow the unitary evolution, which guarantees the full many body state always keeps a constant entropy as its initial one. In comparison, the local subsystems exhibit relaxation behavior and evolve towards certain…
By means of a scaling ansatz, we investigate an approximated solution of the Boltzmann-Vlasov equation for a classical gas. Within this framework, we derive the frequencies and the damping of the collective oscillations of a harmonically…
In a wide class of physical systems, diffeomorphisms in the state space leave the amount of entropy produced per unit time inside the bulk of the system unaffected [M. Polettini et al., 12th Joint European Thermodynamics Conference,…
Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick (LMG)…
This short book is an elementary course on entropy, leading up to a calculation of the entropy of hydrogen gas at standard temperature and pressure. Topics covered include information, Shannon entropy and Gibbs entropy, the principle of…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…
We derive the dark energy fluid equation of state $P = -\epsilon = {\rm const.}$ as an extremum of entropy, subject to the Hamiltonian constraint of General Relativity. However, we identify perturbations that can render this extremum an…
We study the statistical behavior of multimoded optical systems under equilibrium conditions. We investigate the role of variations of the system parameters in the thermodynamic description and derive, an optical analogue of the first law…
An explanation of the mechanism of irreversible dynamics was offered. The explanation was obtained within the framework of laws of classical mechanics by the expansion of Hamilton formalism. Such expansion consisted in adaptation of it to…
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…
A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action. This formulation is extended to the quantum…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
We report the statistical properties of classical particles in (2+1) gravity as resulting from numerical simulations. Only particle momenta have been taken into account. In the range of total momentum where thermal equilibrium is reached,…
This paper addresses fundamental aspects of statistical mechanics such as the motivation of a classical state space with spontaneous transitions, the meaning of non-equilibrium in the context of thermalization, and the justification of…
In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…