We propose a novel trading framework based on entropy-gradient prediction applied tomarket-neutral financial time series. Grounded in principles from statistical physics and information theory, our hypothesis asserts that in approximately closed financial systems, entropy tends to increase over time—implying a directional bias in asset price dynamics. We formalize this idea by modeling small perturbations in return distributions and comparing their impact on Shannon entropy. A large-scale empirical evaluation across 29 equity, sectoral, international, and fixed income ETF spreads reveals that the entropy-gradient signal performs consistentlywell in macro-hedged or structurally distinct pairings. Results show Sharpe ratios up to 0.86and meaningful returns in semi-stable systems, even in the absence of transaction cost modelingor risk overlays. These findings highlight entropy as a second-order probabilistic signal and open avenues for entropy-aware modeling across finance, particularly in systematic strategies where conventional price-based signals fail.