Foundations of Statistical Mechanics: A Deductive Treatment

By O. Penrose. 2005

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Nonadditive entropy: The concept and its use (2008, background): “An entropy S({pi}) is said additive [7] if, for a system composed by any two probabilistically independent subsystems A and B (i.”
Thermodynamics with Continuous Information Flow (2014, methodology): “[32] O. Penrose, Foundations of Statistical Mechanics: A Deductive Treatment (Pergamon, Oxford, England, 1970).”
The lattice Boltzmann method for complex flows (2007, background): “A proof of the above theorem can be found in [46].”
Thermodynamics of information (2015, unknown): “Applying Jensen’s inequality to equation (7), one obtains the inequality (5).”
A Gentle Stochastic Thermostat for Molecular Dynamics (2009, background): “If the process generated by (8)–(10) is ergodic, then a generalization of Birkhoff’s ergodic theorem [2, 15, 25, 26] implies that long trajectories can be used to sample any static observable with respect to the measure ρ β , i.”
Black hole thermodynamical entropy (2012, background): “In other words, according to the definition of entropic additivity in [61], Sq is additive if q = 1, and nonadditive otherwise.”