H-theorem and entropy dissipation estimates in kinetic equations
speaker: Giuseppe Toscani (Università di Pavia)abstract:
In a founding paper Cercignani 1 stated a conjecture about Boltzmann's entropy production for the full Boltzmann equation which would imply an exponentially fast trend to equilibrium, a conjecture almost exhaustively proven seventeen years later by the author with Villani 2. A prominent role in the proof is played by the Fokker-Planck kinetic equation, a model which has recently applied to study relaxation to equilibrium in socio-
economic phenomena 3. In this talk, after a short review of some classical result about entropy production estimates, we show how Boltzmann's strategy can be fruitfully applied
to study the trend to equilibrium in the new field of econophysics 4.
1 Cercignani, C. (1982). H-theorem and trend to equilibrium in the kinetic theory of gases. Archiwum
Mechaniki Stosowane, 34, 231.
2 Toscani, G. and Villani, C. (1999). Sharp entropy production bounds and explicit rate of trend to equi-
librium for the spatially homogeneous Boltzmann equation. Communications in Mathematical Physics,
203, 667.
3 Furioli, G., Pulvirenti, A., Terraneo, E., and Toscani, G. (2017). Fokker{Planck equations in the mod-
elling of socio-economic phenomena, Mathematical Models and Methods in Applied Sciences, 27, 115.
4 Furioli, G., Pulvirenti, A., Terraneo, E., and Toscani, G. (2017) Non-Maxwellian kinetic equations
modeling the evolution of wealth distribution. Mathematical Models and Methods in Applied Sciences,
30, 685.
timetable:
Wed 30 Nov, 9:30 - 10:30, Sala Azzurra
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