Stochastic thermodynamics

Results in Stochastic thermodynamics

• A sharp universal skewness bound for unicyclic currents

  ProvedPtaszyński's conjectured interval −1/16 ≤ C₃/C₁ ≤ 1 for unicyclic Markov currents

  Mathematical physics · Stochastic thermodynamics · standalone Lean package

  For the net crossing count of a marked edge on every finite bidirectional Markov ring with n ≥ 3 states, positive rates and unequal forward and reverse rate products, −1/16 ≤ C₃/C₁ ≤ 1, and both constants are sharp.

  Manuscript: A sharp universal skewness bound for unicyclic currents · Lean proof: A sharp universal skewness bound for unicyclic currents · Verification: A sharp universal skewness bound for unicyclic currents

• A three-state thermal counterexample to a heat-current kurtosis conjecture

  CounterexamplePtaszyński's heat-current kurtosis bound C₄/C₂ ≥ 0 for thermal Markov systems

  Mathematical physics · Stochastic thermodynamics · standalone Lean package

  An explicit three-state, two-bath thermal rate model with local detailed balance has spectral heat-cumulant ratio C₄/C₂ = −3470947982622836/176627429595846691 < 0, contradicting Eq. (19) in its tilted-generator form.

  Manuscript: A three-state thermal counterexample to a heat-current kurtosis conjecture · Lean proof: A three-state thermal counterexample to a heat-current kurtosis conjecture · Verification: A three-state thermal counterexample to a heat-current kurtosis conjecture