Constantin Carathéodory and the axiomatic thermodynamics

Axiomatic Definition of Entropy for Nonequilibrium States

In introductory courses and textbooks on elementary thermodynamics, entropy is often presented as a property defined only for equilibrium states, and its axiomatic definition is almost invariably given in terms of a heat to temperature ratio, the traditional Clausius definition. Teaching thermodynamics to undergraduate and graduate students from all over the globe, we have sensed a need for mor...

An axiomatic foundation for continuum thermodynamics

Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies.

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Pro...

Alternative Axiomatic Characterizations of the Grey Shapley Value

The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapl...

Numeric Experiments in Relativistic Thermodynamics: A Moving System Appears Cooler

In this paper we simulate a two dimensional relativistic ideal gas by implementing a relativistic elastic binary collision algorithm. We show that the relativistic gas faithfully obeys Jüttner’s speed distribution function. Furthermore, using this numeric simulation in conjunction with the energy equipartition theorem for a relativistic gas, we conclude that a moving system appears cooler.