Derives Boltzmann factor from coarse-graining-scale invariance and energy-shift invariance in Hamiltonian systems, fixes parameter by mean energy, and checks against simulations of gases and lattices.
On the energy translation invariance of probability distributions
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abstract
We comment on the problem of energy translation invariance of probability distribution and present some observations. It is shown that a probability distribution can be invariant in the thermodynamic limit if there is no long term interaction or correlation and no relativistic effect. So this invariance should not be considered as a universal theoretical property. Some peculiarities within the invariant $q$-exponential distribution reveal that the connection of the current nonextensive statistical mechanics to thermodynamics might be disturbed by this invariance.
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cond-mat.stat-mech 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Boltzmann Distribution from Invariance of Coarse-Graining-Scale and Energy-Shift
Derives Boltzmann factor from coarse-graining-scale invariance and energy-shift invariance in Hamiltonian systems, fixes parameter by mean energy, and checks against simulations of gases and lattices.