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Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
(Mini-batch) Stochastic Gradient Descent is a popular optimization method which has been applied to many machine learning applications. But a rather high variance introduced by the stochastic gradient in each step may slow down the…
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at…
We study nonequilibrium properties of small and chaotic quantum systems, i.e., non-integrable systems whose size is small in the sense that the separations of energy levels are non-negligible as compared with other relevant energy scales.…
Optimal processes in stochastic thermodynamics are a frontier for understanding the control and design of non-equilibrium systems, with broad practical applications in biology, chemistry, and nanoscale/mesoscale systems. Optimal mass…
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…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
Physical systems driven away from equilibrium by an external controller dissipate heat to the environment; the excess entropy production in the thermal reservoir can be interpreted as a "cost" to transform the system in a finite time. The…
What are the fundamental limitations placed by the laws of thermodynamics on the energy expenditure needed to carry out a given task in a nonequilibrium environment in finite time? In this thesis, we investigate "optimal nonequilibrium…
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…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
We present an Imitation Learning approach for the control of dynamical systems with a known model. Our policy search method is guided by solutions from MPC. Typical policy search methods of this kind minimize a distance metric between the…
In this paper, we study the thermodynamics of short-range central potentials, namely, the Lee-Wick potential, and the Plasma potential. In the first part of the paper we obtain the numerical solution for the orbits equation for these…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
The present study regards the zeroth order mean field approximation of a dipole-type interaction model, which is analytically solved in the canonical and microcanonical ensembles. After writing the canonical partition function, the free and…
For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects,…
Equilibrium statistics of finite Hamiltonian systems is fundamentally described by the microcanonical ensemble (ME). Canonical, or grand-canonical partition functions are deduced from this by Laplace transform. Only in the thermodynamic…
Recent studies have explored finite-time dissipation-minimizing protocols for stochastic thermodynamic systems driven arbitrarily far from equilibrium, when granted full external control to drive the system. However, in both simulation and…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…