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To reconstruct thermodynamics based on the microscopic laws is one of themost important unfulfilled goals of statistical physics. Here, we show that thefirst law and the second law for adiabatic processes are derived from anassumption that "probability distributions of energy in Gibbs states satisfylarge deviation", which is widely accepted as a property of thermodynamicequilibrium states. We define an adiabatic transformation as a randomizedenergy-preserving unitary transformations on the many-body systems and the workstorage. As the second law, we show that an adiabatic transformation from a setof Gibbs states to another set of Gibbs states is possible if and only if theregularized von Neumann entropy becomes large. As the first law, we show thatthe energy loss of the thermodynamic systems during the adiabatictransformation is stored in the work storage as "work," in the followingmeaning; (i) the energy of the work storage takes certain valuesmacroscopically, in the initial state and the final state. (ii) the entropy ofthe work storage in the final state is macroscopically equal to the entropy ofthe initial state. As corollaries, our results give the principle of maximamwork and the first law for the isothermal processes.

Large Deviation implies First and Second Laws of Thermodynamics