Dear Colleagues,

This is an invitation to contribute to the Special Issue "Second Law: Survey and Application". The Second Law launches with two verbal formulations concerning irreversible cyclic processes of discrete systems: The principle of Kelvin (1882) and that of Clausius (1861, 1865). In the meantime, there are "as many formulations of the Second Law as there are authors" (Hutter 1977). Nevertheless, Clausius' extended inequality of irreversible processes in open discrete systems is still today a foundation of the Second Law, if it is formulated by use of time differentials. Two other versions of the Second Law are mentioned, that of Caratheodory (1909) in Bernstein's modification (1960) and that of Sears/Kestin (1963/1970). Essential tools were developed which improve our understanding of discrete systems interacting with their environment: Contact quantities belonging to the discrete system which replace controlling items of the environment; accompanying processes which elucidate the meaning of reversible processes; extension of the Second Law to negative absolute temperatures.

Classical non-linear field theories contain balance equations belonging to physically relevant quantities, such as entropy (of course in non-equilibrium). The entropy balance equation connects the time derivative of the entropy density with the entropy flux density, the entropy supply and the entropy production density. Except of the entropy supply, these quantities are constitutive fields, that means, their special shape depends on the material in consideration. In addition to the entropy balance, the balances of mass, energy and momentum and, if necessary, those of spin, internal variables and other ones for complex materials have to be taken into account. These balance equations form a system of underdetermined differential equations which has to be supplemented by constitutive equations. Dependent on the material, a state space has to be chosen which represents the domain of all fields generating a well posed system of differential equations whose solution is wanted under the constraint that the field of the entropy production density is not negative. This constraint represents the Second Law of the thermodynamical field theory.

The coinage of thermodynamical field theories is many-sided: Different state spaces are used in irreversible thermodynamics, extended thermodynamics, higher gradient and weakly nonlocal thermodynamics and thermodynamics of heat conduction, of surfaces and interfaces, and of complex systems; different exploitation procedures of the non-negative entropy production density in extended and irreversible extended thermodynamics; and different standards in relativistic thermodynamics.

Evolution criteria and GENERIC are other theoretical approaches to thermodynamics apart from thermodynamical field theories. The Second Law plays a central role in all phenomenological thermodynamical theories because it describes the macroscopic Zeitpfeil of the considered system. But on a microscopic stochastic level, there are processes of temporal negative process entropy (Jarzynski 1977), denoted as "violations" of the Second Law, a name which is not correct because the (macroscopic) Second Law is also valid in stochastic thermodynamics as a statistical mean–value.

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• different formulations of the Second Law
• continuum thermodynamics and discrete systems
• constitutive theory: methods of exploiting the dissipation inequality
• irreversible thermodynamics
• extended thermodynamics
• higher gradient theories
• weakly nonlocal thermodynamics
• constitutive theory of heat conduction
• complex systems
• internal variables
• evolution criteria and GENERIC
• Second Law in stochastic and relativistic thermodynamics