1 Master equation system: N units with z micro-states (same - PowerPoint PPT Presentation

1 Master equation system: N units with z micro-states (same energy) : number of units in state ………. probability to find a unit in state 1 z 2 time evolution: ………….. redistribution through state transitions Master equation transitions probability in each time step leaving entering transition rate

2 Master equation - detailed balance detailed balance fixed point: condition: ergodicity each unit reaches eventually all microstates time reversal symmetry after many transitions rates are equal for both directions of transition ………. 1 z 2

3 Master equation - detailed balance detailed balance example state dependent quantity mean value: "position" time evolution: quantity: "density inhomogeneity" detailed balance detailed balance "homogeneous density"

4 Master equation - closed system system: N units with z micro-states characterized by energy distribution: closed system energy fixed equilibrium: maximize with constraints equilibrium thermodynamics internal energy entropy

5 Master equation - closed system energy conservation with H time reversal symmetry maximal detailed balance:

6 Master equation - irreversible process 2 subsystems each in equilibrium, 1 2 weakly coupled total equilibrium entropy of total system: sum of subsystems deviation from total equilibrium weak coupling: relaxation towards equilibrium