We find a unique way of realizing inflation through cyclic phases in a universe with negative vacuum energy. According to the second law of thermodynamics entropy monotonically increases from cycle to cycle, typically by a constant factor. This means that the scale factor at the same energy density in consecutive cycles also increases by a constant factor. If the time period of the oscillations remains approximately constant then this leads to an “overall” exponential growth of the scale factor, mimicking inflation. A graceful exit from this inflationary phase is possible as a dynamical scalar field can take us from the negative to a positive energy vacuum during the last contracting phase.