Related papers: Typicality, entropy and the generalization of stat…
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…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…
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…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
The physical foundations of a variety of emerging technologies --- ranging from the applications of quantum entanglement in quantum information to the applications of nonequilibrium bulk and interface phenomena in microfluidics, biology,…
Few parameters dependent generalised entropy includes Tsallis entropy, R{\'e}nyi entropy, Sharma-Mittal entropy, Barrow entropy, Kaniadakis entropy, etc as particular representatives. Its relation to physical systems is not always clear. In…
Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigen- states of system and its environment…
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
Why is thermalisation a universal phenomenon? How does a quantum system reach thermodynamical equilibrium? These questions are not new, dating even from the very birth of quantum theory and have been the subject of a renewed interest over…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…
Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we note that in physical systems one of these axioms may be violated. For non-ergodic…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
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…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
The theory of small-system thermodynamics was originally developed to extend the laws of thermodynamics to length scales of nanometers. Here we review this "nanothermodynamics," and stress how it also applies to large systems that subdivide…