Related papers: Numerical calculation of the combinatorial entropy…
The entropies of molecules in solution are routinely calculated using gas phase formulae. It is assumed that, because implicit solvation models are fitted to reproduce free energies, this is sufficient for modeling reactions in solution.…
We present an algorithm to estimate the configurational entropy $S$ of a polymer. The algorithm uses the statistics of coincidences among random samples of configurations and is related to the catch-tag-release method for estimation of…
We propose a new recursive procedure to estimate the microcanonical density of states in multicanonical Monte Carlo simulations which relies only on measurements of moments of the energy distribution, avoiding entirely the need for energy…
This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager…
Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…
The thesis focuses on the prediction of solvation thermodynamics using integral equation theories. Our main goal is to improve the approach using a rational correction. We achieve it by extending recently introduced pressure correction, and…
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…
Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This…
We consider the standard thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely…
Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or…
We present an exact microcanonical formulation, in the thermodynamic limit, for a system of $N$ noninteracting particles with $p$ equally spaced energy levels $\{0,\epsilon,2\epsilon,\ldots,(p-1)\epsilon\}$. Writing the microcanonical…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems, even if the Hamiltonian is smooth. The relation…
We apply estimation theory to a system formed by two interacting trapped ions. By using the Fisher matrix formalism, we introduce a simple scheme for estimation of the temperature of the longitudinal vibrational modes of the ions. We use…
Entropy and free-energy estimation are key in thermodynamic characterization of simulated systems ranging from spin models through polymers, colloids, protein structure, and drug-design. Current techniques suffer from being model specific,…
We investigate the memory properties of discrete sequences built upon a finite number of states. We find that the block entropy can reliably determine the memory for systems modeled as Markov chains of arbitrary finite order. Further, we…
This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical…
The excess entropy of restricted primitive model electrolytes is calculated using a potential based approach through the symmetric Poisson-Boltzmann and the modified Poisson-Boltzmann theories. The theories are utilized in conjunction with…
We formulate, under general conditions, the problem of maximisation of the total entropy of the system, assumed to be in a composable form, for fixed total value of the constrained quantity. We derive the general form of the composability…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…