Neo-Gibbsian statistical energetics with applications to nonequilibrium cells

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Physical Chemistry

Background:

• Gibbs' statistical thermodynamics, a century-old theory, governs equilibrium systems.
• Understanding nonequilibrium systems, like living cells, remains a challenge.
• Fluctuations play a crucial role in mesoscopic systems.

Purpose of the Study:

• To generalize Gibbs' statistical thermodynamics through novel interpretations.
• To derive new thermodynamic variational formulae and information entropy functions.
• To develop a new energetics framework for nonequilibrium systems, particularly living cells.

Main Methods:

• Identifying the classical limit (k_B → 0) of Gibbs' theory to derive equilibrium formulae.
• Analyzing the derivative of Gibbs' free energy with respect to temperature to reveal mesoscopic energetics.
• Combining inequalities to define an irreversible thermodynamic potential (ψ) for nonequilibrium states.

Main Results:

• Derived thermodynamic variational formulae governing equilibrium.
• Identified two information entropy functions emerging from mesoscopic energetics.
• Established an irreversible thermodynamic potential (ψ ≥ 0) for nonequilibrium states, reflecting the Second Law of Thermodynamics.
• Proposed ψ as a measure of deviation from equilibrium for living cells.

Conclusions:

• The generalized theory provides a unified framework for equilibrium and nonequilibrium thermodynamics.
• The irreversible thermodynamic potential (ψ) offers a new perspective on the energetics of living cells.
• This work bridges statistical mechanics with the complex dynamics of biological systems.