Large Deviation implies First and Second Laws of Thermodynamics

Understand

To reconstruct thermodynamics based on the microscopic laws is one of the most important unfulfilled goals of statistical physics.

• Here, we show that the first law and the second law for adiabatic processes are derived from an assumption that "probability distributions of energy in Gibbs states satisfy large deviation", which is widely accepted as a property of thermodynamic equilibrium states.
• We define an adiabatic transformation as a randomized energy-preserving unitary transformations on the many-body systems and the work storage.
• As the second law, we show that an adiabatic transformation from a set of Gibbs states to another set of Gibbs states is possible if and only if the regularized von Neumann entropy becomes large.