Generalization of the second law for a transition between nonequilibrium states

The maximum work formulation of the second law of thermodynamics is generalized for a transition between nonequilibrium states. The relative entropy, the Kullback-Leibler divergence between the nonequilibrium states and the canonical distribution, determines the maximum ability to work. The difference between the final and the initial relative entropies with an effective temperature gives the maximum dissipative work for both adiabatic and isothermal processes. Our formulation reduces to both the Vaikuntanathan-Jarzynski relation and the nonequilibrium Clausius relation in certain situations. By applying our formulation to a heat engine the Carnot cycle is generalized to a circulation among nonequilibrium states.     

Concept of time in the general law of thermodynamics as the basis of the thermodynamics of the nonequilibrium state

A mathematical formulation is proposed for the general law of thermodynamics in the form of relations defining the concept of thermodynamic time and the criterion of stable equilibrium. It is hypothesized that an implicit function F(, , , , ... ⁽ⁿ⁾)=0 associates the thermodynamic time and the potential of the nonequilibrium state. Partial solutions of a general form are also obtained for the trajectories of a nonequilibrium process, characterized by the presence of only one independent variable, i.e., =(⁽ⁿ⁾).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 49–54, August, 1989.     

Information-theoretical derivation of a nonequilibrium extension of Wien's displacement law

Wien's displacement law for the wavelength of maximum intensity of a blackbody is extended to nonequilibrium systems. A non-vanishing temperature gradient causes a correction in the displacement law that is predicted and estimated making use of information theory. A simple application is presented.     

Relationship between the thermodynamics of nonequilibrium state and the thermodynamics of nonequilibrium processes

The concept and equations of the thermodynamics of nonequilibrium state are compared with the postulates of linear thermodynamics of nonequilibrium processes. It is shown that all the four basic postulates can be obtained as consequences of the equations of the thermodynamics of nonequilibrium state. In the limiting case of small deviations from equilibrium, the thermodynamics of nonequilibrium state are reduced to linear thermodynamics of nonequilibrium processes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 10–14, December, 1990.     

Dimer as a challenge to the second law

A simple system consisting of an asymmetric dimer cooperating with two baths is presented as a challenge to the second law of thermodynamics. This requires specific coupling of the dimer to the baths and a specific thermodynamic regime.Received: 22 March 2003, Published online: 4 August 2003PACS: 05.30.-d Quantum statistical mechanics - 05.70.-a Thermodynamics This articles has been submitted by V. Capek a few weeks before he passed away and it is presumably his last paper. It has been edited by D.P. Sheehan (University of San Diego, USA).     

On the second law of thermodynamics

The second law of thermodynamics has two distinct aspects to its foundations. The first concerns the question of why entropy goes up in the future, and the second, of why it goes down in the past. Statistical physicists tend to be more concerned with the first question and with careful considerations of definition and mathematical detail. The second question is of quite a different nature; it leads into areas of cosmology and quantum gravity, where the mathematical and physical issues are ill understood.     

Average-ion model for calculating the state of a multicomponent transient nonequilibrium highly charged ion plasma

The ionization kinetics of a transient nonequilibrium highly charged ion plasma are investigated in the average-ion approximation. Approximations of a hydrogenic ion, whose energy levels depend either on the principal quantum number alone or on the principal and orbital angular momentum quantum numbers, are considered as atom models. The results of calculations of various plasma characteristics performed within this model are presented, and a comparison with previously published data, as well as with calculations in the chemical-bond approximation, is performed. It is shown that the average-ion model satisfactorily describes the spectral characteristics of a nonideal plasma. Zh. éksp. Teor. Fiz. 111, 496–513 (February 1997)     

Existence of a state function characterizing the level of nonequilibrium of a thermodynamic system

On the basis of the principle of maximum work, it is shown that, on a real trajectory of a nonequilibrium process, the work losses – have a minimum value and can be determined from the relation , where has the meaning of a thermodynamic potential of a nonequilibrium state and, being an extremally determined quantity, is a function of state, and has the properties of an exact differential; A_max is the maximum work of an equilibrium, quasistatic process; A_pos is the possible work of a nonequilibrium process; A is the limiting value of the possible work done in a nonequilibrium process, such that A_max>AA_pos.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 20–23, May, 1989.     

Dimension of inhomogeneous state in nonequilibrium superconductors

Spatially inhomogeneous order parameters are observed in super-conducting Pb-In films under large nonequilibrium injection of quasi-particles via tunneling. Critical sample dimension in which the inhomogeneous state appears is determined for the first time by means of a precise fabrication of tunnel injector and detector, and discussed in terms of several current models.     

Jensen inequality and the second law

Jensen's Inequality (JIEQ) has proved to be a major tool to prove the consistency of various fluctuation theorems with the second law in microscopic nonequilibrium thermodynamics. We show that the situation is far from clear and the reliance on the JIEQ may be quite misleading in general.     

Exact nonequilibrium steady state of a strongly driven open XXZ chain

An exact and explicit ladder-tensor-network ansatz is presented for the nonequilibrium steady state of an anisotropic Heisenberg XXZ spin-1/2 chain which is driven far from equilibrium with a pair of Lindblad operators acting on the edges of the chain only. We show that the steady-state density operator of a finite system of size n is-apart from a normalization constant-a polynomial of degree 2n - 2 in the coupling constant. Efficient computation of physical observables is facilitated in terms of a transfer operator reminiscent of a classical Markov process. In the isotropic case we find cosine spin profiles, 1/n(2) scaling of the spin current, and long-range correlations in the steady state. This is a fully nonperturbative extension of a recent result [Phys. Rev. Lett. 106, 217206 (2011)].     

Quantum approach to a derivation of the second law of thermodynamics

We reinterpret the microcanonical conditions in the quantum domain as constraints for the interaction of the "gas subsystem" under consideration and its environment ("container"). The time average of a purity measure is found to equal the average over the respective path in Hilbert space. We then show that for typical (degenerate or nondegenerate) thermodynamical systems almost all states within the allowed region of Hilbert space have a local von Neumann entropy S close to the maximum and a purity P close to its minimum, respectively. Typically, thermodynamical systems should obey the second law.     

A new approach to the properties of a harmonic crystal in a stationary nonequilibrium state

An exact analytical solution has been obtained for the covariance matrix resulting from a stochastic interaction of a linear chain ofN coupled harmonic oscillators with different heat reservoirs via its endparticles. For the special case, that the friction forces on the endparticles, which result from the system-heatbath-interaction, are equal, we obtain the same results as Lebowitz et al. by applying an entirely different mathematical technique as these authors have used. For the realistic coupling, where friction and diffusion coefficient differ for different heatbaths and are only connected via the Einstein relation we obtain additional contributions to the correlation matrices between the momenta and between the displacements.On leave from the School of Nuclear Engineering, The University of New South Wales, Sydney, Australia     

Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state

We investigate the total entropy production of a Brownian particle in a driven bistable system. This system exhibits the phenomenon of stochastic resonance. We show that in the time-periodic steady state, the probability density function for the total entropy production satisfies Seifert’s integral and detailed fluctuation theorems over finite time trajectories.     

A general information theoretical proof for the second law of thermodynamics

It is shown that the conservation and the non-additivity of the information, together with the additivity of the entropy, make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the non-additivity of information is also true in other fields in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true not only in quantum and classical physics but also in other processes in which the information is conservative and non-additive. Supported by the National Natural Science Foundation of China (Grant No. 10305001)