Related papers: Entropy and the second law for driven, or quenched…
The classical Second Law of Thermodynamics demands that an isolated system evolves with a non-diminishing entropy. This holds as well in quantum mechanics if the evolution of the energy-isolated system can be described by a unital quantum…
A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum…
The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
Thermodynamics allows the application of Statistical Mechanics to finite and even small systems. As surface effects cannot be scaled away, one has to be careful with the standard arguments of splitting a system into two or bringing two…
Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical…
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…
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…
For an isolated assembly that comprises a system and its surrounding reservoirs, the total entropy ($S_{a}$) always monotonically increases as time elapses. This phenomenon is known as the second law of thermodynamics ($S_{a}\geq0$). Here…
The second law of thermodynamics states that the entropy of an isolated system is almost always increasing. We propose combinatorial formalizations of the second law and explore their conditions of possibilities.
We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by the…
It exists a large class of systems for which the traditional notion of extensivity breaks down. From experimental examples we induce two general hypothesis concerning such systems. In the first the existence of an internal coordinate system…
We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact…
Entropy is critically examined as a fundamental concept in contemporary science and informatics. Although the typical Shannon entropy provides a proper framework for describing the canonical ensemble, it fails to represent adequately the…
We analyze a gas of noninteracting fermions confined to a one-dimensional harmonic oscillator potential, with the aim of distinguishing between two proposed definitions of the thermodynamic entropy in the microcanonical ensemble, namely the…
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…
It is known that the equilibrium properties of open classical systems that are strongly coupled to a heat bath are described by a set of thermodynamic potentials related to the system's Hamiltonian of mean force. By adapting this framework…
The Second Law of Thermodynamics states that the entropy of a closed system is non-decreasing. Discussing the Second Law in the quantum world poses new challenges and provides new opportunities, involving fundamental…
The physical meaning of entropy is analyzed in the context of statistical, nuclear, atomic physics and cosmology. Only the microcanonical Boltzmann entropy leads to no contradictions in several simple, elementary and for thermodynamics…
A question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume (volume entropy, also known as the Gibbs entropy) or as the logarithm of the density of states…