Related papers: Quantropy
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…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
Exploring the analogy between quantum mechanics and statistical mechanics we formulate an integrated version of the Quantropy functional [1]. With this prescription we compute the propagator associated to Boltzmann-Gibbs statistics in the…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the…
A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
The paper examines and critiques the expression of entropy as the logarithm of the number of quantum states of a physical system. Boltzmann method of expressing entropy as the logarithm of the number of states of a gas with a given total…
The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics…
A microscopic understanding of the thermodynamic entropy in quantum systems has been a mystery ever since the invention of quantum mechanics. In classical physics, this entropy is believed to be the logarithm of the volume of phase space…
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 consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
The statistical problem of the distribution of $s$ quanta of equal energy $\epsilon_0$ and total energy $E$ among $N$ distinguishable particles is resolved using the conventional theory based on Boltzmann's principle of equal probabilities…
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
The equipartition theorem is a fundamental law of classical statistical physics, which states that every degree of freedom contributes $k_{B}T/2$ to the energy, where $T$ is the temperature and $k_{B}$ is the Boltzmann constant. Recent…
Relaxation dynamics of complex quantum systems with strong interactions towards the steady state is a fundamental problem in statistical mechanics. The steady state of subsystems weakly interacting with their environment is described by the…
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…