A method for online assessing a state of health (SOH) of an electrochemical cell, comprises a step for estimating the state of health (SOH) of the electrochemical cell from thermodynamics data related to the cell the thermodynamics data including entropy and enthalpy variations ΔS, ΔH within the cell. A system for fast-charging a rechargeable battery with terminals connected to internal electrochemical cells, comprises a power supply connected to the rechargeable battery and arranged for applying a time-varying charging voltage to the battery terminals, a charging-control processor for controlling the power supply, and a system for online assessing a state of health (SOH) of the battery, the SOH assessment system comprising means for estimating the state of health (SOH) of the electrochemical cell from thermodynamics data related to the battery.