Related papers: Minimal Work Principle and its Limits for Classica…
In mechanics, common energy principles are based on fixed boundary conditions. However, in bridge engineering structures, it is usually necessary to adjust the boundary conditions to make the structure's internal force reasonable and save…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
We derive an equality for non-equilibrium statistical mechanics in finite-dimensional quantum systems. The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the presence of a Markovian heat bath. It…
Lagrangian mechanics uses d'Alembert's principle of zero virtual work as an important starting point. The orthogonality of the force of constraint and virtual displacement is emphasized in literature, without a clear warning that this is…
To what extent do thermodynamic resource theories capture physically relevant constraints? Inspired by quantum computation, we define a set of elementary thermodynamic gates that only act on 2 energy levels of a system at a time. We show…
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…
The approximation of integral type functionals is studied for discrete observations of a continuous It\^o semimartingale. Based on novel approximations in the Fourier domain, central limit theorems are proved for $L^2$-Sobolev functions…
The Second Law of Thermodynamics asserts that the physical entropy of an adiabatic system is an increasing function in time. In this paper we will study a more stringent version of this law, according to which the entropy should not only…
Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve nonzero power for the practical extraction of work, these processes must be performed within a finite time, which inevitably induces…
Equalities are generally more suitable for experimental verification than inequalities. In this work, I derive valid equalities from the Euler-Lagrange equation for the optimization of macroscopic thermodynamic averages in weakly driven…
There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both…
The second law of thermodynamics states that for a thermally isolated system entropy never decreases. Most physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger…
Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion…
We determine the maximal work extractable via a cyclic Hamiltonian process from a positive-temperature ($T>0$) microcanonical state of a $N\gg 1$ spin bath. The work is much smaller than the total energy of the bath, but can be still much…
Physical devices operating out of equilibrium are inherently affected by thermal fluctuations, limiting their operational precision. This issue is pronounced at microscopic and especially quantum scales and can only be mitigated by…
The Hybrid Minimum Principle (HMP) is established for the optimal control of deterministic hybrid systems with both autonomous and controlled switchings and jumps where state jumps at the switching instants are permitted to be accompanied…
Thermodynamics constrains changes to the energy of a system, both deliberate and random, via its first and second laws. When the system is not in equilibrium, fluctuation theorems such as the Jarzynski equality further restrict the…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical…