A toy model is used to describe the following steps to achieve the no-reversible-direction axiom in a tutorial manner: (i) choose a state space results in the balance equations on state space which ...are linear in the process directions, (ii) avoid a reversible process direction that cannot be generated via a combination of non-reversible ones, (iii) process directions that are in the kernel of the balance equations and do not enter the entropy production. The Coleman–Mizel formulation of the second law and the Liu relations follow immediately.
Creating a modified Belinfante/Rosenfeld procedure, Mathisson-Papapetrou-like equations are derived by which a comparison of General-Covariant Continuum Physics (GCCP) with General Relativity Theory ...(GRT) becomes possible. Three cases emerge: If the energy-momentum tensor of GCCP is symmetric and divergence-free, it serves as source of Einstein's equation; if the energy-momentum tensor is non-symmetric or/and not divergence-free, GRT and GCCP are incompatible with each other, if the Mathisson-Papapetrou-like equations are not valid; if they are valid, a source of Einstein's equation can be generated which is different from the energy-momentum tensor of GCCP.
Non-equilibrium and equilibrium thermodynamics of an interacting component in a relativistic multi-component system is discussed covariantly by exploiting an entropy identity. The special case of the ...corresponding free component is considered. Equilibrium conditions and especially the multi-component Killing relation of the 4-temperature are discussed. Two axioms characterize the mixture: additivity of the energy momentum tensors and additivity of the 4-entropies of the components generating those of the mixture. The resulting quantities of a single component and of the mixture as a whole, energy, energy flux, momentum flux, stress tensor, entropy, entropy flux, supply and production are derived. Finally, a general relativistic 2-component mixture is discussed with respect to their gravitation generating energy–momentum tensors.
Meixner's historical remark in 1969 "... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined..." is ...investigated from today's insight. Several statements-such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness-are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment.
Non-equilibrium and equilibrium thermodynamics of an interacting component of a special-relativistic multi-component system is discussed by using an entropy identity. The special case of the ...corresponding free component is considered.
The connection between endoreversible models of Finite-Time Thermodynamics and the corresponding real running irreversible processes is investigated by introducing two concepts which complement each ...other:
and
. In that context, the importance of particular machine diagrams for
and (reconstruction) parameter diagrams for
is emphasized. Additionally, the treatment of internal irreversibilities through the use of contact quantities like the contact temperature is introduced into the Finite-Time Thermodynamics description of thermal processes.
Internal and mesoscopic variables differ fundamentally from each other: both are state space variables, but mesoscopic variables are additionally equipped with a distribution function introducing a ...statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of the liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as a mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers.
How to introduce thermodynamics to quantum mechanics? From numerous possibilities of solving this task, the simple choice is here: the conventional von Neumann equation deals with a density operator ...whose probability weights are time-independent. Because there is no reason apart from the reversible quantum mechanics that these weights have to be time-independent, this constraint is waived, which allows one to introduce thermodynamical concepts to quantum mechanics. This procedure is similar to that of Lindblad's equation, but different in principle. But beyond this simple starting point, the applied thermodynamical concepts of discrete systems may perform a 'source theory' for other versions of phenomenological quantum thermodynamics. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.
The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems that are those systems for which sub-systems are out of ...consideration. Taking sub-systems into account, as it is by definition necessary for decomposed systems, the interaction Hamiltonians –which are absent in undecomposed systems– can be a source of irreversibility in decomposed systems. Thus, the following two-stage task arises: How to modify von Neumann’s equation of undecomposed systems so that irreversibility appears, and how this modification affects decomposed systems? The first step was already done in Muschik (“Concepts of phenomenological irreversible quantum thermodynamics: closed undecomposed Schottky systems in semi-classical description,”
, vol. 44, pp. 1–13, 2019) and is repeated below, whereas the second step to formulate a quantum thermodynamics of decomposed systems is performed here by modifying the von Neumann equations of the sub-systems by a procedure wich is similar to that of Lindblad’s equation (G. Lindblad, “On the generators of quantum dynamical semigroups,”
, vol. 48, p. 119130, 1976), but different because the sub-systems interact with one another through partitions.
How to introduce thermodynamics to quantum mechanics? From numerous possibilities of solving this task, the simple choice is here: the conventional von Neumann equation deals with a density operator ...whose probability weights are time-independent. Because there is no reason apart from the reversible quantum mechanics that these weights have to be time-independent, this constraint is waived, which allows one to introduce thermodynamical concepts to quantum mechanics. This procedure is similar to that of Lindblad’s equation, but different in principle. But beyond this simple starting point, the applied thermodynamical concepts of discrete systems may perform a ‘source theory’ for other versions of phenomenological quantum thermodynamics.
This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.
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