Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to – justified or not – hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann) we demonstrate how the corresponding entropy has to look like, given the form of the corresponding distribution functions. By two natural assumptions that (i) t...

Lecture 1. Free Independence and Free Harmonic Analysis. 2 1.1. Probability spaces. 2 1.2. Non-commutative probability spaces. 3 1.3. Classical independence. 4 1.4. Free products of non-commutative probability spaces. 5 1.5. Free Fock space. 6 1.6. Free Central Limit Theorem. 8 1.7. Free Harmonic Analysis. 10 1.8. Further topics. 16 Lecture 2. Random Matrices and Free Probability. 17 2.1. Rando...

The brain is a complex structure made up of interconnected neurons, and its electrical activities can be evaluated using electroencephalogram (EEG) signals. The characteristics of the brain area affected by partial epilepsy can be studied using focal and non-focal EEG signals. In this work, a method for the classification of focal and non-focal EEG signals is presented using entropy measures. T...

We explore the role a non-Markovian memory kernel plays on information exchange and entropy production in context of external work protocol. The Jarzynski equality is shown to hold for both harmonic nonharmonic models. observe function acts as an pump, recovering part lost thermal reservoir consequence nonequilibrium pumping action occurs cases. Unexpectedly, we found that model does not produc...