Related papers: Thermodynamics and evolutionary biology through op…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
At very small scales, thermodynamic energy exchanges like work and heat become comparable to thermal energy of the system, which leads to unusual phenomena like the transient violations of Second Law. We explore the generic characters of…
The general maximum principle is proved for an infinite dimensional controlled stochastic evolution system. The control is allowed to take values in a nonconvex set and enter into both drift and diffusion terms. The operator-valued backward…
There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson…
Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing…
How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative…
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small nonequilibrium systems. While work and heat are equally important forms of energy exchange, fluctuation relations have not been experimentally…
The key element of the approach to the theory of necessary conditions in optimal control discussed in the paper is reduction of the original constrained problem to unconstrained minimization with subsequent application of a suitable…
We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This…
The essence of the second law of classical thermodynamics is the `entropy principle' which asserts the existence of an additive and extensive entropy function, S, that is defined for all equilibrium states of thermodynamic systems and whose…
The second law of thermodynamics constitutes a fundamental principle of physics, precluding the existence of perpetual motion machines and providing a natural definition of the arrow of time. Its scope extends across virtually all areas of…
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…
On the one hand, the dissipated heat of a thermodynamic work extraction process upper bounds the non-predictive information, which the associated system encodes about its environment. Thus, emergent information processing capabilities can…
Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the…
The appeal of thermodynamics to problems outside physics is undeniable, as is the growing recognition of its apparent universality, yet in the absence of a rigorous formalism divorced from the peculiarities of molecular systems all attempts…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
Non-equilibrium thermodynamics with internal variables introduces a natural hierarchical arrangement of evolution equations. Three examples are shown: a hierarchy of linear constitutive equations in thermodynamic rhelogy with a single…
We derive a formulation of the First Law of nonequilibrium thermodynamics for biological information-processing systems by partitioning entropy in the Second Law into microscopic and mesoscopic components and by assuming that natural…
Equilibrium thermodynamics is combined with Jarzynski's irreversible work theorem to quantify the excess entropy produced by irreversible processes. The resulting rectified form of the second law parallels the first law, in the sense that…
A general, uniform, rigorous and constructive thermodynamic approach to weakly nonlocal non-equilibrium thermodynamics is reviewed. A method is given to construct and restrict the evolution equations of physical theories according to the…