Related papers: Gaussian concentration bound and Ensemble equivale…
The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature $T$. However, non-negligible interactions between system and environment can give rise to an altered state. Here we derive…
Equilibrium Statistical Mechanics is undoubtedly a cornerstone for the description of many particle systems. The common interpretation is based on ensemble theory as put forward by Gibbs, alongside the basic assumptions that different…
Grand-canonical fluctuations of Bose-Einstein condensates of light are accessible to state-of-the-art experiments [J. Schmitt et al., Phys. Rev. Lett. 112, 030401 (2014).]. We phenomenologically describe these fluctuations by using the…
We consider a regular chain of elementary quantum systems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of…
It is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the…
This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…
We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs in an external conservative force field, that is environments described by the Generalized or Gibbs canonical ensemble. We demonstrate…
We introduce "local uncertainty relations" in thermal many body systems. Using these relations, we derive basic bounds. These results include the demonstration of universal non-relativistic speed limits (regardless of interaction range),…
We studied the escort averages in microcanonical and canonical ensembles in the Tsallis statistics of entropic parameter $q>1$. The quantity $(q-1)$ is the measure of the deviation from the Boltzmann-Gibbs statistics. We derived the…
We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of $N$ interacting fermions with charge conservation, or $N$ interacting spins with one conserved component of total spin. We define an effective…
We discuss the dynamics and thermodynamics of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system to the canonical description of a stochastically forced Brownian system. We…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
The clustering property of an equilibrium bipartite correlation is one of the most general thermodynamic properties in non-critical many-body quantum systems. Herein, we consider the thermalization properties of a system class exhibiting…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
We study the transition probabilities of a two-point measurement on a quantum system, initially prepared in a thermal state. We find two independent constraints on the difference between transition probabilities when the system is prepared…
A statistical treatment of finite unbound systems in the presence of collective motions is presented and applied to a classical Lennard-Jones Hamiltonian, numerically simulated through molecular dynamics. In the ideal gas limit, the flow…
For quantum systems that are weakly coupled to a much 'bigger' environment, thermalization of possibly far from equilibrium initial ensembles is demonstrated: for sufficiently large times, the ensemble is for all practical purposes…
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…
In finite many-body quantum systems such as nuclei, atoms, mesoscopic systems like quantum dots and small metallic grains, interacting spin systems modeling quantum computing core and BEC, the interparticle interactions are essentially…
We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at an effective temperature gives a good description of the steady state provided that…