Related papers: Enhancing the understanding of entropy through com…
From a new rigorous formulation of the general axiomatic foundations of thermodynamics we derive an operational definition of entropy that responds to the emergent need in many technological frameworks to understand and deploy thermodynamic…
Phase transitions in nuclei, small atomic clusters and self-gravitating systems demand the extension of thermo-statistics to ``Small'' systems. The main obstacle is the thermodynamic limit. It is shown how the original definition of the…
Classical particle systems characterized by continuous size polydispersity, such as colloidal materials, are not straightforwardly described using statistical mechanics, since fundamental issues may arise from particle distinguishability.…
Computational complexity is a particularly important objective. The idea of Landauer principle was extended through mapping three classic problems (sorting,ordered searching and max of N unordered numbers) into Maxwell demon thought…
Boltzmann sampling based on Metropolis algorithm has been extensively used for simulating a canonical ensemble. An estimate of a mechanical property, like energy, of an equilibrium system, can be made by averaging over a large number…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…
In analogy to Brownian computers we explicitly show how to construct stochastic models, which mimic the behaviour of a general purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation,…
Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with…
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
The entropy of a system gives a powerful insight into its microscopic degrees of freedom, however standard experimental ways of measuring entropy through heat capacity are hard to apply in mesoscale and nanoscale systems, as they require…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
We present a quantum algorithm for the microcanonical thermal pure quantum (TPQ) method, which has an advantage in evaluating thermodynamic quantities at finite temperatures, by combining with some recently developed techniques derived from…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
The dynamical justifications which lie at the basis of an effective Statistical Mechanics for self gravitating systems are formulated, analyzing some among the well known obstacles thought to prevent a rigorous Statistical treatment. It is…
The paper moves a step towards the full integration of statistical mechanics and information theory. Starting from the assumption that the thermodynamical system is composed by particles whose quantized energies can be modelled as…
Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
Modern thermodynamic theories can be used to study highly complex quantum dynamics. Here, we experimentally demonstrate that the violation of thermodynamic constraints allows to detect the coupling of a quantum system to a hidden…
The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, traditionally only the canonical and grand canonical ensembles have been used. In this…