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Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important…
Jarzynski Equality (JE) and the thermodynamic integration method are conventional methods to calculate free energy difference (FED) between two equilibrium states with constant temperature of a system. However, a number of ensemble samples…
The estimate of free energy changes based on Bennett's acceptance ratio method is examined in several limiting cases and compared with other estimates based on the Jarzynski equality and on the Crooks relation. While the absolute amount of…
We show how thermodynamic properties of molecular models can be computed over a large, multidimensional parameter space by combining multistate reweighting analysis with a linear basis function approach. This approach reduces the…
This paper is concerned with the problem of state estimation for discrete-time linear systems in the presence of additional (equality or inequality) constraints on the state (or estimate). By use of the minimum variance duality, the…
Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
We present a new method to evaluate vibrational free energies of atomic systems without a priori specification of an interatomic potential. Our model-agnostic approach leverages descriptors, high-dimensional feature vectors of atomic…
Host-guest binding plays a crucial role in the functionality of various systems, and its efficiency is often quantified using the binding free energy, which represents the free-energy difference between the bound and dissociated states.…
In this thesis we examine methodologies for determining free energy differences (FEDs) of phases via Monte Carlo simulation. We identify and address three generic issues that arise in FED calculations; the choice of representation, the…
State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…
The computation of free energy differences through an exponential weighting of out of equilibrium paths (known as the Jarzynski equality) is often used for transitions between states described by an external parameter $\lambda$ in the…
Metadynamics is a commonly used and successful enhanced sampling method. By the introduction of a history dependent bias which depends on a restricted number of collective variables(CVs) it can explore complex free energy surfaces…
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy…
The free energy landscapes of several fundamental processes are characterized by high barriers separating long-lived metastable states. In order to explore these type of landscapes enhanced sampling methods are used. While many such methods…
According to the Jarzynski theorem, equilibrium free energy differences can be calculated from the statistics of work carried out during non-equilibrium transformations. Although exact, this approach can be plagued by large statistical…
With the help of metadynamics it is possible to calculate efficiently the free energy of systems displaying high energy barriers as a function of few selected "collective variables". In doing this, the contribution of all the other degrees…
Thermodynamic phase transitions, a central concept in physics and chemistry, are typically controlled by an interplay of enthalpic and entropic contributions. In most cases, the estimation of the enthalpy in simulations is straightforward…
Extracting equilibrium information from nonequilibrium measurements is a challenge task of great importance in understanding the thermodynamic properties of physical, chemical, and biological systems. The discovery of the Jarzynski equality…