
In 1854 Clausius proved the famous theorem that bears his name by assuming the second “law” of thermodynamics. In the present paper we give a proof that requires no such assumption. Our proof rests on the laws of mechanics, a T-mixing property, an ergodic consistency condition, and on the axiom of causality. Our result relies on some recently derived theorems, such as the Evans-Searles and the Crooks fluctuation theorems and the recently discovered relaxation and dissipation theorems.
Time reversible, Chemical thermodynamics and energetics, Ergodics, Systems, Fluctuation theorem, Keywords: Consistency conditions, Crooks fluctuation theorem, Microscopic dynamics, Physical sciences, Engineering, Chemical sciences, Free energy differences, Thermodynamics, 3100 Physics and Astronomy, Work relation, 1606 Physical and Theoretical Chemistry, Theorem proving
Time reversible, Chemical thermodynamics and energetics, Ergodics, Systems, Fluctuation theorem, Keywords: Consistency conditions, Crooks fluctuation theorem, Microscopic dynamics, Physical sciences, Engineering, Chemical sciences, Free energy differences, Thermodynamics, 3100 Physics and Astronomy, Work relation, 1606 Physical and Theoretical Chemistry, Theorem proving
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