Related papers: Enhancing the understanding of entropy through com…
We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Heat capacity measurements are a powerful tool that researchers rely on when studying the relationship between microscopic degrees of freedom and macroscopic behavior in condensed matter. This uniqueness stems from heat capacity capturing…
It has been suggested recently that the microcanonical entropy of a system may be accurately reproduced by including a logarithmic correction to the canonical entropy. In this paper we test this claim both analytically and numerically by…
The thermodynamics and microstructure of confined fluids with small particle number are best described using the canonical ensemble. However, practical calculations can usually only be performed in the grand-canonical ensemble, which can…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter,…
Using the stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time dependent temperature, in which case the systems are permanently out of thermodynamic…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic…
In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This…
By making use of a recently proposed framework for the inference of thermodynamic irreversibility in bosonic quantum systems, we experimentally measure and characterize the entropy production rates in the non-equilibrium steady state of two…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
We analyze the dynamics of a simple but nontrivial classical Hamiltonian system of infinitely many coupled rotators. We assume that this infinite system is driven out of thermal equilibrium either because energy is injected by an external…
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to…
This thesis reports progress in two domains, causal structures and microscopic thermodynamics, both of which are pertinent in the development of quantum technologies. The first part is dedicated to the analysis of causal structure, which…
We combine machine learning (ML) with Monte Carlo (MC) simulations to study the crystal nucleation process. Using ML, we evaluate the canonical partition function of the system over the range of densities and temperatures spanned during…
It is shown that quantum systems of identical particles can be treated as if they were different when they are in well differentiated states. This simplifying assumption allows the consideration of quantum systems isolated from the rest of…