The overwhelming majority of maximum entropy production applications to ecological and environmental systems are based on thermodynamics and statistical physics. Here, we discuss briefly maximum entropy production principle and raises two questions: (i) can this principle be used as the basis for non-equilibrium thermodynamics and statistical mechanics and (ii) is it possible to 'prove' the pri...

In recent years a growing number of philosophers of science have come to realise that the philosophical foundations of statistical mechanics are not as secure as was once thought. Conceptual problems that had been swept under a carpet of technicalities, or simply ignored, have surfaced, solutions that were accepted are being questioned, and new routes are being explored. Thus, central issues su...

Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einstein's formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. ...

15.1. The First Law of Thermodynamics • Define the first law of thermodynamics. • Describe how conservation of energy relates to the first law of thermodynamics. • Identify instances of the first law of thermodynamics working in everyday situations, including biological metabolism. • Calculate changes in the internal energy of a system, after accounting for heat transfer and work done. 15.2. Th...

The time evolution during which macroscopic systems reach thermodynamic equilibrium states proceeds as a continuous sequence of contact structure preserving transformations maximizing the entropy. This viewpoint of mesoscopic thermodynamics and dynamics provides a unified setting for the classical equilibrium and nonequilibrium thermodynamics, kinetic theory, and statistical mechanics. One of t...

Black holes have their own thermodynamics including notions of entropy and temperature and versions of the three laws. After a light introduction to black hole physics, I recollect how black hole thermodynamics evolved in the 1970’s, while at the same time stressing conceptual points which were given little thought at that time, such as why the entropy should be linear in the black hole’s surfa...